5 coins are tossed together. What is the probability of getting exactly 4 heads?
Solution
Total outcomes = 2^5 = 32.
Favourable = 5. Probability = 5/32.
Answer: (B) 5/32
Quantitative Aptitude · Counting and probability
Probability: MAH CET, NMAT and SNAP practice questions
20 questions in the pattern of MAH MBA CET, NMAT and SNAP. Each question is marked with the exams it suits. Answer it, then open the step-by-step solution.
Exam:
A box has 5 red and 4 blue balls. Three balls are drawn at random. What is the probability that all three are red?
Solution
Total = C(9, 3) = 84.
Favourable = C(5, 3) = 10. Probability = 5/42.
Answer: (D) 5/42
A card is drawn from a well-shuffled pack of 52. What is the probability that it is a red king?
Solution
Favourable cards = 2.
Probability = 2/52 = 1/26.
Answer: (B) 1/26
The odds in favour of an event are 7 : 6. What is the probability that the event happens?
Solution
Probability = favourable/(favourable + unfavourable) = 7/13.
Answer: (B) 7/13
A bag has 4 red, 5 blue and 3 green balls. Two balls are drawn at random. What is the probability that one is red and one is blue?
Solution
Total ways = C(12, 2) = 66; favourable = 20.
Probability = 20/66 = 10/33.
Answer: (B) 10/33
The probabilities that A and B solve a problem are 2/3 and 3/4. If they try independently, what is the probability that both of them solve it?
Solution
P(A) = 2/3, P(B) = 3/4.
Required probability = 1/2.
Answer: (A) 1/2
A box has 7 red and 5 blue balls. Three balls are drawn at random. What is the probability that at least one is blue?
Solution
Total = C(12, 3) = 220.
Favourable = C(12, 3) − C(7, 3) = 185. Probability = 37/44.
Answer: (C) 37/44
Bag I has 6 red and 4 black balls; bag II has 6 red and 6 black balls. A bag is chosen at random and a ball is drawn. What is the probability that it is red?
Solution
P(red) = ½ × 6/10 + ½ × 6/12 = 11/20.
Answer: (D) 11/20
A number is picked at random from 1 to 30. What is the probability that it is divisible by 5 or 2?
Solution
By 5: 6; by 2: 15; by both: 3.
Count = 18; probability = 3/5.
Answer: (A) 3/5
A bag has 7 red, 6 blue and 4 green balls. Two balls are drawn at random. What is the probability that one is red and one is blue?
Solution
Total ways = C(17, 2) = 136; favourable = 42.
Probability = 42/136 = 21/68.
Answer: (D) 21/68
Two cards are drawn together from a pack of 52. What is the probability that both are red?
Solution
Total ways = C(52, 2) = 1326; favourable = 325.
Probability = 25/102.
Answer: (C) 25/102
4 coins are tossed together. What is the probability of getting at least 2 heads?
Solution
Total outcomes = 2^4 = 16.
Favourable = 11. Probability = 11/16.
Answer: (B) 11/16
Two dice are thrown. What is the probability of getting a prime number as the sum?
Solution
Of the 36 outcomes, 15 are favourable.
Probability = 5/12.
Answer: (D) 5/12
Two dice are thrown. What is the probability of getting a doublet (the same number on both dice)?
Solution
Of the 36 outcomes, 6 are favourable.
Probability = 1/6.
Answer: (C) 1/6
A letter is chosen at random from the word COMMITTEE. What is the probability that it is M?
Solution
M appears 2 times among 9 letters.
Probability = 2/9.
Answer: (D) 2/9
Two dice are thrown. What is the probability that the sum is equal to 9?
Solution
There are 36 equally likely outcomes.
Favourable outcomes: 4. Probability = 4/36 = 1/9.
Answer: (A) 1/9
A card is drawn from a well-shuffled pack of 52. What is the probability that it is a heart or a face card?
Solution
Favourable cards = 22.
Probability = 22/52 = 11/26.
Answer: (B) 11/26
Two dice are thrown. What is the probability that the sum is less than 10?
Solution
There are 36 equally likely outcomes.
Favourable outcomes: 30. Probability = 30/36 = 5/6.
Answer: (A) 5/6
What is the probability that a leap year, chosen at random, has 53 Mondays?
Solution
A leap year has 52 weeks and 2 extra days.
Probability that the extra day(s) include a Monday = 2/7.
Answer: (D) 2/7
7 people sit in a row at random. What is the probability that two particular people sit next to each other?
Solution
Total = 7!; together = 2 × (7 − 1)!.
Probability = 2/7 = 2/7.
Answer: (B) 2/7
These are original practice questions written by Target Campus in the pattern and difficulty of MAH MBA CET, NMAT, SNAP and other MBA entrance tests. They are not previous-year papers.
Preparing for MAH CET, NMAT, SNAP or CAT? Courses, live classes and mocks by Dr. Kiran Derle at Target Campus.
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