PlacementPrepTwo dice are thrown together. What is the probability that the sum is 7?
Solution
There are 36 equally likely outcomes.
Pairs that add to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) — 6 pairs.
Probability = 6/36 = 1/6.
Answer: (C) 1/6
Quantitative Aptitude · Counting
Probability: placement practice questions
30 moderate questions in the pattern of campus placement tests. Pick an option to check your answer, then open the step-by-step solution.
A bag contains 6 red and 5 blue balls. Two balls are drawn at random. What is the probability that both are red?
Solution
Ways to choose 2 red = C(6, 2) = 15; ways to choose any 2 = C(11, 2) = 55.
Probability = 15/55 = 3/11.
Answer: (D) 3/11
A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is a red card?
Solution
Favourable cards = 26.
Probability = 26/52 = 0.5.
Answer: (A) 0.5
3 coins are tossed together. What is the probability of getting exactly 1 head?
Solution
Total outcomes = 23 = 8.
Ways to get exactly 1 head = C(3, 1) = 3.
Probability = 0.375.
Answer: (C) 0.375
The probabilities that A and B solve a problem are 1/3 and 0.25. If both try independently, what is the probability that the problem is solved?
Solution
Probability that neither solves = (1 − 1/3) × (1 − 0.25) = 0.5.
Solved = 1 − 0.5 = 0.5.
Answer: (C) 0.5
A number is picked at random from 1 to 20. What is the probability that it is divisible by 3 or 5?
Solution
Divisible by 3: 6; by 5: 4; by both (15): 1.
Count = 6 + 4 − 1 = 9, so probability = 0.45.
Answer: (A) 0.45
Two dice are thrown together. What is the probability that the sum is 4?
Solution
There are 36 equally likely outcomes.
Pairs that add to 4: (1,3), (2,2), (3,1) — 3 pairs.
Probability = 3/36 = 1/12.
Answer: (D) 1/12
A bag contains 3 red and 4 blue balls. Two balls are drawn at random. What is the probability that both are red?
Solution
Ways to choose 2 red = C(3, 2) = 3; ways to choose any 2 = C(7, 2) = 21.
Probability = 3/21 = 1/7.
Answer: (C) 1/7
A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is a face card?
Solution
Favourable cards = 12.
Probability = 12/52 = 3/13.
Answer: (C) 3/13
The probabilities that A and B solve a problem are 2/3 and 0.75. If both try independently, what is the probability that the problem is solved?
Solution
Probability that neither solves = (1 − 2/3) × (1 − 0.75) = 1/12.
Solved = 1 − 1/12 = 11/12.
Answer: (D) 11/12
A number is picked at random from 1 to 20. What is the probability that it is divisible by 5 or 2?
Solution
Divisible by 5: 4; by 2: 10; by both (10): 2.
Count = 4 + 10 − 2 = 12, so probability = 0.6.
Answer: (C) 0.6
Two dice are thrown together. What is the probability that the sum is 10?
Solution
There are 36 equally likely outcomes.
Pairs that add to 10: (4,6), (5,5), (6,4) — 3 pairs.
Probability = 3/36 = 1/12.
Answer: (B) 1/12
A bag contains 6 red and 7 blue balls. Two balls are drawn at random. What is the probability that both are red?
Solution
Ways to choose 2 red = C(6, 2) = 15; ways to choose any 2 = C(13, 2) = 78.
Probability = 15/78 = 5/26.
Answer: (D) 5/26
4 coins are tossed together. What is the probability of getting exactly 1 head?
Solution
Total outcomes = 24 = 16.
Ways to get exactly 1 head = C(4, 1) = 4.
Probability = 0.25.
Answer: (A) 0.25
The probabilities that A and B solve a problem are 0.5 and 1/3. If both try independently, what is the probability that the problem is solved?
Solution
Probability that neither solves = (1 − 0.5) × (1 − 1/3) = 1/3.
Solved = 1 − 1/3 = 2/3.
Answer: (D) 2/3
A number is picked at random from 1 to 100. What is the probability that it is divisible by 3 or 2?
Solution
Divisible by 3: 33; by 2: 50; by both (6): 16.
Count = 33 + 50 − 16 = 67, so probability = 67/100.
Answer: (B) 67/100
A bag contains 4 red and 5 blue balls. Two balls are drawn at random. What is the probability that both are red?
Solution
Ways to choose 2 red = C(4, 2) = 6; ways to choose any 2 = C(9, 2) = 36.
Probability = 6/36 = 1/6.
Answer: (C) 1/6
A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is a spade or an ace?
Solution
Favourable cards = 16 (13 spades + 3 other aces).
Probability = 16/52 = 4/13.
Answer: (D) 4/13
3 coins are tossed together. What is the probability of getting exactly 2 heads?
Solution
Total outcomes = 23 = 8.
Ways to get exactly 2 heads = C(3, 2) = 3.
Probability = 0.375.
Answer: (B) 0.375
The probabilities that A and B solve a problem are 0.25 and 0.4. If both try independently, what is the probability that the problem is solved?
Solution
Probability that neither solves = (1 − 0.25) × (1 − 0.4) = 0.45.
Solved = 1 − 0.45 = 0.55.
Answer: (C) 0.55
A number is picked at random from 1 to 20. What is the probability that it is divisible by 3 or 2?
Solution
Divisible by 3: 6; by 2: 10; by both (6): 3.
Count = 6 + 10 − 3 = 13, so probability = 0.65.
Answer: (D) 0.65
Two dice are thrown together. What is the probability that the sum is 6?
Solution
There are 36 equally likely outcomes.
Pairs that add to 6: (1,5), (2,4), (3,3), (4,2), (5,1) — 5 pairs.
Probability = 5/36 = 5/36.
Answer: (C) 5/36
A bag contains 4 red and 4 blue balls. Two balls are drawn at random. What is the probability that both are red?
Solution
Ways to choose 2 red = C(4, 2) = 6; ways to choose any 2 = C(8, 2) = 28.
Probability = 6/28 = 3/14.
Answer: (B) 3/14
4 coins are tossed together. What is the probability of getting exactly 3 heads?
Solution
Total outcomes = 24 = 16.
Ways to get exactly 3 heads = C(4, 3) = 4.
Probability = 0.25.
Answer: (D) 0.25
A number is picked at random from 1 to 20. What is the probability that it is divisible by 2 or 7?
Solution
Divisible by 2: 10; by 7: 2; by both (14): 1.
Count = 10 + 2 − 1 = 11, so probability = 0.55.
Answer: (B) 0.55
Two dice are thrown together. What is the probability that the sum is 5?
Solution
There are 36 equally likely outcomes.
Pairs that add to 5: (1,4), (2,3), (3,2), (4,1) — 4 pairs.
Probability = 4/36 = 1/9.
Answer: (A) 1/9
A bag contains 7 red and 7 blue balls. Two balls are drawn at random. What is the probability that both are red?
Solution
Ways to choose 2 red = C(7, 2) = 21; ways to choose any 2 = C(14, 2) = 91.
Probability = 21/91 = 3/13.
Answer: (D) 3/13
A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is a king?
Solution
Favourable cards = 4.
Probability = 4/52 = 1/13.
Answer: (D) 1/13
A number is picked at random from 1 to 30. What is the probability that it is divisible by 5 or 7?
Solution
Divisible by 5: 6; by 7: 4; by both (35): 0.
Count = 6 + 4 − 0 = 10, so probability = 1/3.
Answer: (A) 1/3
A card is drawn from a well-shuffled pack of 52 cards. What is the probability that it is a king or a queen?
Solution
Favourable cards = 8.
Probability = 8/52 = 2/13.
Answer: (A) 2/13
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