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55+ Probability Aptitude Questions with Solution | Examples and Tricks

Probability Questions

Frequently asked 55+ Probability Aptitude Questions on dice, cards, balls, bags etc are given here and it covers almost all the types of questions related to Probability topic that are mostly asked in the competitive examination. Probability Questions with Solutions are mentioned here along with solved examples. Candidates will also know about the tricks that are involved in solving Probability Questions and Answers.

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Strategies and Tricks to Solve Probability Questions:

Probability of an event : P(event) = Number of favourable outcomes/Total number of outcomes

  • If the probability of happening an event is x then the probability of not happening that event is (1-x).
  • For e.g., If the probability of winning a game is 0.4 then the probability of loosing it is (1-0.4) = 0.6
  • If the probability of finding a defective bulb is 3/7 then the probability of finding a non-defective bulb is (1-3/7) = 4/7.

Tips and Tricks to Solve Probability Questions:

In a deck of playing cards, there are four types of cards :
♠ (Spades in Black colour) having A, 2,3,4,5,6,7,8,9,10,J,K, and Q total 13 cards
♣ (Clubs in Black colour) having A, 2,3,4,5,6,7,8,9,10,J,K, and Q total 13 cards
♥ (Hearts in Red colour) having A, 2,3,4,5,6,7,8,9,10,J,K, and Q total 13 cards
♦ (Diamond in Red colour) having A, 2,3,4,5,6,7,8,9,10,J,K, and Q total 13 cards
52 cards

Jack, King and Queen are known as ‘Face Cards’, As these cards are having some pictures on it. Always remember Ace is not a face card as it doesn’t carry any face on it.

  • If one coin is tossed the total number of outcomes is 2 either a Head or a Tail.
  • If two coins are tossed the total number of outcomes is 2 ×2 = 4
  • If three coins are tossed the total number of outcomes is 2 ×2×2 = 8
  • Similarly, for Dice, In a single roll total number of outcomes are 6
  • If two Dices are rolled, a total number of outcomes is 6×6 = 36

Probability Solved Examples:

Example 1: What is the probability of getting a sum of 7 when two dice are thrown?
Solution: Probability math – Total number of ways = 6 × 6 = 36 ways. Favorable cases = (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3) — 6 ways. P (A) = 6/36 = 1/6

Example 2: A coin is thrown 3 times .what is the probability that atleast one head is obtained?
Solution: Sample space = [HHH, HHT, HTH, THH, TTH, THT, HTT, TTT]
Total number of ways = 2 × 2 × 2 = 8.  Fav. Cases = 7
P (A) = 7/8
OR
P (of getting at least one head) = 1 – P (no head)⇒ 1 – (1/8) = 7/8

Example 3: Two cards are drawn from the pack of 52 cards. Find the probability that both are diamonds or both are kings.
Solution: Total no. of ways = 52C2
Case I: Both are diamonds = 13C2
Case II: Both are kings = 4C2
P (both are diamonds or both are kings) = (13C2 + 4C2 ) / 52C2

Get here: 21+ Geometry Practice Questions

Example 4: Find the probability of getting two heads when five coins are tossed.
Solution: Number of ways of getting two heads = 5C2 = 10. Total Number of ways = 25 = 32
P (two heads) = 10/32 = 5/16

Example 5: From a pack of cards, three cards are drawn at random. Find the probability that each card is from different suit.
Solution: Total number of cases = 52C3
One card each should be selected from a different suit. The three suits can be chosen in 4C3 was
The cards can be selected in a total of (4C3) x (13C1) x (13C1) x (13C1)
Probability = 4C3 x (13C1)3 / 52C3
= 4 x (13)3 / 52C3

Example 6: Fifteen people sit around a circular table. What are odds against two particular people sitting together?
Solution: 15 persons can be seated in 14! Ways. No. of ways in which two particular people sit together is 13! × 2!
The probability of two particular persons sitting together 13!2! / 14! = 1/7
Odds against the event = 6 : 1

Example 7: Two dice are thrown together. What is the probability that the number obtained on one of the dice is multiple of number obtained on the other dice?
Solution: Total number of cases = 62 = 36
Since the number on a die should be multiple of the other, the possibilities are
(1, 1) (2, 2) (3, 3) —— (6, 6) — 6 ways
(2, 1) (1, 2) (1, 4) (4, 1) (1, 3) (3, 1) (1, 5) (5, 1) (6, 1) (1, 6) — 10 ways
(2, 4) (4, 2) (2, 6) (6, 2) (3, 6) (6, 3) — 6 ways
Favorable cases are = 6 + 10 + 6 = 22. So, P (A) = 22/36 = 11/18

Example 8: Find the probability of getting a numbered card when a card is drawn from the pack of 52 cards.
Solution: Total Cards = 52. Numbered Cards = (2, 3, 4, 5, 6, 7, 8, 9, 10) 9 from each suit 4 × 9 = 36
P (E) = 36/52 = 9/13

Check Out: Average Aptitude Questions with Answers

Example 9: What is the probability of getting a sum of 7 when two dice are thrown?
Solution: Probability math – Total number of ways = 6 × 6 = 36 ways. Favorable cases = (1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3) — 6 ways. P (A) = 6/36 = 1/6

Example 10: 1 card is drawn at random from the pack of 52 cards.
(i) Find the Probability that it is an honor card.
(ii) It is a face card.
Solution: (i) honor cards = (A, J, Q, K) 4 cards from each suits = 4 × 4 = 16
P (honor card) = 16/52 = 4/13
(ii) face cards = (J,Q,K) 3 cards from each suit = 3 × 4 = 12 Cards.
P (face Card) = 12/52 = 3/13

Probability Questions

Probability Questions With Solutions

Question 1) Two coins are tossed, find the probability that two heads are obtained.
Note: Each coin has two possible outcomes H (heads) and T (Tails).
Solution:
The sample space S is given by.
S = {(H,T),(H,H),(T,H),(T,T)}
Let E be the event “two heads are obtained”.
E = {(H,H)}
We use the formula of the classical probability.
P(E) = n(E) / n(S) = 1 / 4

Question 2) Two dice are rolled, find the probability that the sum is
a) equal to 1
b) equal to 4
c) less than 13
Solution:
a) The sample space S of two dice is shown below.
S = { (1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6) }
Let E be the event “sum equal to 1”. There are no outcomes which correspond to a sum equal to 1, hence
P(E) = n(E) / n(S) = 0 / 36 = 0
b) Three possible outcomes give a sum equal to 4: E = {(1,3),(2,2),(3,1)}, hence.
P(E) = n(E) / n(S) = 3 / 36 = 1 / 12
c) All possible outcomes, E = S, give a sum less than 13, hence.
P(E) = n(E) / n(S) = 36 / 36 = 1

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Question 3) A card is drawn at random from a deck of cards. Find the probability of getting the 3 of diamond.
Solution: Let E be the event “getting the 3 of diamond”. An examination of the sample space shows that there is one “3 of diamond” so that n(E) = 1 and n(S) = 52. Hence the probability of event E occurring is given by
P(E) = 1 / 52

Question 4) A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn from the jar at random, what is the probability that this marble is white?
Solution: We first construct a table of frequencies that gives the marbles color distributions as follows

ColorFrequency
red3
green7
white10

We now use the empirical formula of the probability
P(E) = Frequency for white color / Total frequencies in the above table
= 10 / 20 = 1 / 2

Question 5) A die is rolled, find the probability that an even number is obtained.
Solution: Let us first write the sample space S of the experiment.
S = {1,2,3,4,5,6}
Let E be the event “an even number is obtained” and write it down.
E = {2,4,6}
We now use the formula of the classical probability.
P(E) = n(E) / n(S) = 3 / 6 = 1 / 2

Question 6) Which of these numbers cannot be a probability?
Solution:  A probability is always greater than or equal to 0 and less than or equal to 1, hence only a) and c) above cannot represent probabilities: -0.00010 is less than 0 and 1.001 is greater than 1.

Get Here: Simplification and Approximation Questions

Question 7) A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the coin shows a head.
Solution:  Let H be the head and T be the tail of the coin. The sample space S of the experiment described in question 5 is as follows
S = { (1,H),(2,H),(3,H),(4,H),(5,H),(6,H)
(1,T),(2,T),(3,T),(4,T),(5,T),(6,T)}
Let E be the event “the die shows an odd number and the coin shows a head”. Event E may be described as follows
E={(1,H),(3,H),(5,H)}
The probability P(E) is given by
P(E) = n(E) / n(S) = 3 / 12 = 1 / 4

Question 8) A card is drawn at random from a deck of cards. Find the probability of getting a queen.
Solution: The sample space S of the experiment in question 7 is shwon above (see question 6)
Let E be the event “getting a Queen”. An examination of the sample space shows that there are 4 “Queens” so that n(E) = 4 and n(S) = 52. Hence the probability of event E occurring is given by
P(E) = 4 / 52 = 1 / 13

Question 9) The blood groups of 200 people is distributed as follows: 50 have type A blood, 65 have B blood type, 70 have O blood type and 15 have type AB blood. If a person from this group is selected at random, what is the probability that this person has O blood type?
Solution: We construct a table of frequencies for the the blood groups as follows

GroupFrequency
a50
B65
O70
AB15

We use the empirical formula of the probability
P(E) = Frequency for O blood / Total frequencies
= 70 / 200 = 0.35

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Question 10) Find the probability of selecting a black card or a 6 from a deck of 52 cards.

Solution: We need to find out P(B or 6)

Probability of selecting a black card  = 26/52

Probability of selecting a 6 = 4/52

Probability of selecting both a black card and a 6 = 2/52

P(B or 6) = P(B) + P(6) – P(B and 6)

= 26/52 + 4/52 – 2/52

= 28/52

= 7/13.

Probability Practice Questions With Answers

Question 1) Six individual sock are present in a drawer- Two Red, Two Black and Two White. Pradeep picked one sock randomly to wear. Now he draws another sock from the drawer then what is the probability he draws a sock of same color?

1.1/5
2. 1/6
3. 1/30
4. 11/30
5. None

Question 2) Anil placed a deck of 52 cards. If you pick two cards what is the probability that both are aces?
1. 1/169
2. 1/221
3. 1/338
4. 4/663
5. None

Question 3) You have drawn a card from 52 cards deck. without replacing it you have drawn another card. Then what is the probability of that card to be King of Diamond?
1. 1/51
2. 1/52
3. 2/51
4. 3/52
5. None

Question 4) A bag contains 100 tickets, numbered from 1 to 100. If three tickets are picked at random and with replacement, what is the probability that sum of three numbers on the tickets will even number?
1. 1/2
2. 3/4
3. 1/8
4. 3/8
5. None

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Question 5) A Bag contains some White and Black Balls. The probability of picking two white balls one after other without replacement from that bag is 14/33. Then what will be the probability of picking two Black balls from that Bag if bag can hold maximum 15 balls only?
1. 11/32
2. 14/33
3. 7/33
4. 1/11
5. Cannot be determined

Question 6) Bag A contains 7 Red Balls, ‘X’ Green Balls, and 5 Yellow Balls. The probability to pick Green Ball at random is 2/5. Another Bag B contains ‘X-3’ Red Balls, ‘X-4’ Yellow Balls and 6 Green Balls. If two balls are picked one after the other from Bag B at random then what is the probability for the Balls to be Red?
1. 1/21
2. 2/21
3. 3/21
4. 4/21
5. Cannot be determined

Question 7) Born babies to be boy is having 0.52 probability, and to be girl is 0.48. If you have two children, then what is the probability that they are both girls?
1. 0.2304
2. 0.2704
3. 0.2496
4. 0.7696
5. None

Question 8) Suppose children like three types of chocolates Perk, Munch, and 5 Star. If they are asked to choose to pick chocolate they have their own preference, one-sixth of children population preference is Perk>Munch>5star. One-sixth of children population preference is Munch>5star>Perk. Similarly remaining four-sixths children preferences follows as per above combinations. If you met a random child and give him chance to pick a chocolate between Munch and Perk. He picked Munch. Now you offer Munch and 5star, what is the probability that he chooses again Munch?
1. 1/6
2. 1/2
3. 2/3
4. 3/4
5. None

Question 9) Tickets numbered from 1 to 40 are in a bag and one ticket is drawn at random. What is the probability that ticket drawn is a multiple of 3 or 7?
1. 15/30
2. 16/30
3. 17/30
4. 18/30
5. None

Question 10) There are three boxes each containing 3 Pink and 5 Yellow balls and also there are 2 boxes each containing 4 Pink and 2 Yellow balls. A Yellow ball is selected at random. Find the probability that Yellow ball is from a box of the first group?
A. 42/61
B. 45/61
C. 51/61
D. 52/61
E. None of these

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Question 11) A committee of five persons is to be chosen from a group of 10 people. The probability that a certain married couple will either serve together or not at all is?
1. 54/199
2. 52/195
3. 53/186
4. 51/126
5. None of these

Question 12) Three Bananas and three oranges are kept in a box. If two fruits are chosen at random, Find the probability that one is Banana and another one is orange?
1. 1/5
2. 3/5
3. 4/5
4. 2/5
5. None of these

Question 13) A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If three balls are picked at random, what is the probability that two are Black and one is Green?
1. 22/355
2. 15/381
3. 10/393
4. 14/455
5. 18/455

Question 14) A basket contains 6 White 4 Black 2 Pink and 3 Green balls.If two balls are picked at random, what is the probability that either both are Pink or both are Green?
1. 2/105
2. 4/105
3. 8/137
4. 5/137
5. None of these

Question 15) A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both hearts. Find the Probability of the lost card being a heart?
1. 12/50
2. 8/50
3. 11/50
4. 9/50
5. None of these

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Question 16) A fruit basket contains 10 Guavas and 20 Bananas out of which 3 Guavas and 5 Bananas are defective. If two fruits selected at random, what is the probability that either both are Bananas or both are non-defective?
1. 315/435
2. 313/435
3. 317/435
4. 316/435
5. None of these

Question 17) Out of 14 applicants for a job, there are 6 women and 8 men. It is desired to select 2 persons for the job. The probabilty that atleast one of selected persons will be a Woman is?
1. 77/91
2. 54/91
3. 45/91
4. 40/91
5. None of these

Question 18) A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If three balls picked up random, What is the probability that all three are White?
1. 4/91
2. 5/93
3. 7/97
4. 8/92
5. None of these

Question 19) A basket contains 6 White 4 Black 2 Pink and 3 Green balls. If four balls are picked at random, what is the probability that atleast one is Black?
1. 69/91
2. 80/91
3. 21/91
4. 55/91
5. None of these

Question 20) In a bag there are 4 white, 4 red and 2 green balls. Two balls are drawn at random.What is the probability that at least one ball is of red colour?
1. 4/3
2. 7/3
3. 1/3
4. 2/3
5. None of these

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Question 21) In an examination, there are three sections namely Reasoning, Maths and English. Reasoning part contains 4 questions. There are 5 questions in maths section and 6 questions in English section. If three questions are selected randomly from the list of questions then what is the probability that all of them are from maths?
1. 7/91
2. 8/91
3. 2/91
4. 4/91

Question 22) A basket contains 5 red 4 blue 3 green marbles. If three marbles picked up random, What is the probability that at least one is blue?
1. 41/55
2. 53/55
3. 47/55
4. 49/55

Question 23) A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps.If three caps are picked at random, what is the probability that two are red and one is green?
1. 22/55
2. 15/81
3. 10/91
4. 5/91

Question 24) A bag contains 2 red caps, 4 blue caps, 3 yellow caps and 5 green caps. If three caps are picked at random, what is the probability that none is green?
1. 2/13
2. 3/13
3. 1/13
4. 5/13

Question 25) A box contains 27 marbles some are blue and others are green. If a marble is drawn at random from the box, the probability that it is blue is 1/3. Then how many number of green marbles in the box?
1. 10
2. 15
3. 14
4. 18

Get Here: Number Series Question

Question 26) Sahil has two bags (A & B) that contain green and blue balls.In the Bag ‘A’ there are 6 green and 8 blue balls and in the Bag ‘B’ there are 6 green and 6 blue balls. One ball is drawn out from any of these two bags. What is the probability that the ball drawn is blue?
1. 15/28
2. 13/28
3. 17/28
4. 23/28

Question 27) A basket contains 5 red 4 blue 3 green marbles. If three marbles picked up random, What is the probability that either all are green or all are red?
1. 1/20
2. 7/20
3. 3/20
4. 9/20

Question 28) A basket contains 5 red 4 blue 3 green marbles. If two marbles picked up random, What is the probability that both are red?
1. 4/33
2. 5/33
3. 7/33
4. 8/33

Question 29) A bag contains 5 red caps, 4 blue caps, 3 yellow caps and 2 green caps. If four caps are picked at random, what is the probability that two are red, one is blue and one is green?
1. 22/1001
2. 80/1001
3. 21/1001
4. 55/1001

Question 30) P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?
1. 1/3
2. 1/4
3. 1/5
4. 1/6
5. None of these

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Question 31) A box contains 4 red, 5 black and 6 green balls. 3 balls are drawn at random. What is the probability that all the balls are of same colour?
1. 33/455
2. 34/455
3. 44/455
4. 47/455
5. None of these

Question 32) A speak truth in 60% cases and B in 80% cases. In what percent of cases they likely to contradict each other narrating the same incident?
1. 9/25
2. 7/25
3. 11/25
4. 13/25
5. None of these

Question 33) Two person A and B appear in an interview.  The probability of A’s selection is 1/5 and the probability of B’s selection is 2/7. What is the probability that only one of them is selected?

  1. 11/35
  2. 12/35
  3. 13/35
  4. 17/35
  5. None of these

Question 34) A bag contains 6 red balls and 8 green balls. 2 balls are drawn at random one by one with replacement. Find the probability that both the balls are green
1. 16/49
2. 25/49
3. 12/49
4. 21/49
5. None of these

Question 35) A bag contains 5 red and 7 white balls. Four balls are drawn out one by one and not replaced. What is the probability that they are alternatively of different colours?
1. 7/99
2. 11/99
3. 14/99
4. 19/99
5. None of these

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Question 36) 10 persons are seated around a round table. What is the probability that 4 particular persons are always seated together?
1. 1/21
2. 4/21
3. 8/21
4. 11/21
5. None of these

Question 37) An apartment has 8 floors. An elevator starts with 4 passengers and stops at 8 floors of the apartment. What is the probability that all passengers travels to different floors?
1. 109/256
2. 135/256
3. 105/256
4. 95/256
5. None of these

Question 38) A box contains 30 electric bulbs, out of which 8 are defective. Four bulbs are chosen at random from this box. Find the probability that at least one of them is defective?
1. 432/783
2.574/783
3. 209/784
4. 334/784
5. None of these

Question 39) A 4- digit number is formed by the digits 0, 1, 2, 5 and 8 without repetition. Find the probability that the number is divisible by 5.
1. 1/5
2. 2/5
3. 3/5
4. 4/5
5. None of these

Question 40) A bag contains 6 red balls and 7 white balls. Another bag contains 5 red balls and 3 white balls. One ball is selected from each. Find the probability that one ball is red and one is white?
1. 53/104
2. 47/104
3. 63/104
4. 51/104
5. None of these

Solve Out: Percentage Aptitude Questions

Question 41) A card is drawn from a pack of 52 cards. The card is drawn at random; find the probability that it is neither club nor queen?
1. 4/13
2. 5/13
3. 7/13
4. 9/13
5. None of these

Question 42) From a pack of cards, if three cards are drawn at random one after the other with replacement, find the probability that one is ace, one is jack and one is queen?
1. 16/7725
2. 16/5525
3. 18/5524
4. 64/5515
5. None of these

Question 43) Find the probability that in a random arrangement of the letter of words in the word ‘PROBABILITY’ the two I’s come together.
1. 2/11
2.1/11
3.3/11
4. 4/11
5. None of these

Question 44) A bag contains 3 red balls and 8 blacks ball and another bag contains 5 red balls and 7 blacks balls, one ball is drawn at random from either of the bag, find the probability that the ball is red.
1. 93/264
2. 95/264
3.91/264
4. 97/264
5. None of these

Question 45) A six-digit is to be formed from the given numbers 1, 2, 3, 4, 5 and 6. Find the probability that the number is divisible by 4.
1. 3/17
2. 4/15
3. 4/19
4. 4/17
5. None of these

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Question 46) A lottery is organised by the college ABC through which they will provide scholarship of rupees one lakhs to only one student. There are 100 fourth year students, 150 third year students, 200 second year students and 250 first year students. What is the probability that a second year student is choosen.
1. 1/7
2. 2/7
3. 3/7
4. 4/7
5. None of these

Question 47) A box contains 50 balls, numbered from 1 to 50. If three balls are drawn at random with replacement. What is the probability that sum of the numbers are odd?
1. 1/2
2. 1/3
3. 2/7
4. 1/5
5. None of these

Question 48) A and B are two persons sitting in a circular arrangement with 8 other persons. Find the probability that both A and B sit together.
1. 1/9
2. 2/7
3. 2/9
4. 2/5
5. None of these

Question 49) In a race of 12 cars, the probability that car A will win is 1/5 and of car B is 1/6 and that of car C is 1/3.  Find the probability that only one of them won the race.
1. 2/7
2. 7/10
3. 9/10
4. 3/7
5. None of these

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Question 50) 12 persons are seated at a circular table. Find the probability that 3 particular persons always seated together.
1. 9/55
2.7/55
3. 4/55
4. 3/55
5. None of these

Answers:

Ans1) 1Ans18) 1Ans35) 3
Ans2) 2Ans19) 1Ans36) 1
Ans3) 1Ans20) 4Ans37) 3
Ans4) 1Ans21) 3Ans38) 2
Ans5) 4Ans22) 1Ans39) 2
Ans6) 2Ans23) 4Ans40) 2
Ans7) 1Ans24) 2Ans41) 4
Ans8) 3Ans25) 4Ans42) 2
Ans9) 3Ans26) 1Ans43) 1
Ans10) 2Ans27) 1Ans44) 3
Ans11) 4Ans28) 2Ans45) 2
Ans12) 2Ans29) 2Ans46) 2
Ans13) 5Ans30) 4Ans47) 1
Ans14) 2Ans31) 2Ans48) 3
Ans15) 3Ans32) 3Ans49) 2
Ans16) 4Ans33) 3Ans50) 4
Ans17) 1Ans34) 1

The topic Probability is well explained on this page of recruitmentresult.com Candidates can firstly go through the examples, tricks, Solved Probability Questions and then solve out the practice questions and match their selected option with the given answer list, to evaluate their performance.

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