Quantitative Aptitude

Probability

1,860 Questions
All Sample Space Setup 558 Permutation & Combination Counting 288 Multiplication Theorem (AND) 234 Addition Theorem (OR) 151 At Least One Probability 134 Complement Rule (P(Not A)) 130 Drawing Without Replacement 126 Conditional Probability 75 Bayes' Theorem 69 Drawing With Replacement 49 Success and Failure Rates 46

Probability Questions

Multiple choice

What is the number of probable outcomes?

Directions: Read the following information and answer the given question:

Rohan is a school boy and he was confused between completing his homework and watching a live cricket match. So, he decides to toss a coin on a certain flag, which has 4 equal parts of different colours viz. red, blue, green and yellow colours. He comes to the conclusion that he will complete his homework only if the coin falls as a heads on the red colour.

  1. 4

  2. 6

  3. 8

  4. 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

There are 2 outcomes of the coin on every colour. So, 2 outcomes on 4 colours = 2 x 4 = 8 outcomes.

Multiple choice

What is the probability that he is donating at most 2 lakhs?

Directions: Read the following information and answer the given question.

Ram was confused about the amount that he should donate to an old-age home. He decides to toss a coin three times and decides that he will donate as many number of lakhs to the old-age home as the number of tails he gets.

  1. 1/8

  2. 3/8

  3. 5/8

  4. 7/8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

There are 8 possible outcomes as depicted: {hhh, hht, hth, thh, htt, tht, tth, ttt} At most 2 lakhs means that tails occurs at most twice; so the possible outcomes are 7, i.e. {hhh, hht, hth, thh, htt, tht, tth}. The probability that he is donating at most 2 lakhs = 7/8. 

Multiple choice

What is the probability that he will watch cricket?

Directions: Read the following information and answer the given question:

Rohan is a school boy and he was confused between completing his homework and watching a live cricket match. So, he decides to toss a coin on a certain flag, which has 4 equal parts of different colours viz. red, blue, green and yellow colours. He comes to the conclusion that he will complete his homework only if the coin falls as a heads on the red colour.

  1. 1/2

  2. 3/8

  3. 1/4

  4. 7/8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total number of outcomes = 8 (because heads on four colors and tails on four colors) Probability that he will work only when heads will occur on red colour = 1/8 So, probability of watching cricket = 1 – 1/8 = 7/8

Multiple choice

What is the probabilty that he will lose his money this time? He will lose money only if the team loses.

Directions: Read the following information and answer the given question.

Arun, a resident Indian citizen, gambles his money on the World Cup cricket matches. Most of the times he wins money, but when he loses, he starts fighting for the money. This time he has gambled money on the Indian cricket team. The probability of the Indian cricket team winning a match is 0.7. Also, there is a 10% chance that the match will be drawn.

  1. 0.1

  2. 0.2

  3. 0.3

  4. 0.4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Required probability = 1 – 0.7 – 0.1 = 0.2

Multiple choice

What is the probability that he will neither lose nor win? He loses only if the team loses, and wins only if the team wins.

Directions: Read the following information and answer the given question.

Arun, a resident Indian citizen, gambles his money on the World Cup cricket matches. Most of the times he wins money, but when he loses, he starts fighting for the money. This time he has gambled money on the Indian cricket team. The probability of the Indian cricket team winning a match is 0.7. Also, there is a 10% chance that the match will be drawn.

  1. 0.1

  2. 0.15

  3. 0.2

  4. 0.25
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Required probability = 10%/100% = 0.1

Multiple choice

What is the probability that his neice will get a ball in the first go?

Directions: Read the following information and answer the given question.

Amit has a big jar. He puts 12 white, 10 grey and 20 black balls in it. He is playing a game with his son, his neice and his brother. He decides that he will randomly pick a ball from the jar, and when he draws a white ball, he will give it to his neice, grey ball to his brother and black ball to his son. He will continue doing so till the jar has been emptied. The person with the maximum balls will win.

  1. 3/7

  2. 4/7

  3. 2/7

  4. 5/7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Required probability = 12/42 = 2/7

Multiple choice

What is the probability that his son will not get a ball in the first draw?

Directions: Read the following information and answer the given question.

Amit has a big jar. He puts 12 white, 10 grey and 20 black balls in it. He is playing a game with his son, his neice and his brother. He decides that he will randomly pick a ball from the jar, and when he draws a white ball, he will give it to his neice, grey ball to his brother and black ball to his son. He will continue doing so till the jar has been emptied. The person with the maximum balls will win.

  1. 10/21

  2. 11/21

  3. 5/21

  4. 16/21
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Required probability = (12 + 10)/42 = 22/42 = 11/21

Multiple choice

A card is drawn from a pack of 50 cards numbered 1 to 50. Find the probability of drawing a number which is a square.

  1. 1/10

  2. 7/50

  3. 43/50

  4. 3/25

  5. 3/50
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are seven perfect square numbers in the given range. Let A = Event of getting a number, which is a square = ( 1,4,9,16,25,36, 49). Hence, n(A) = 7. There are total 50 cards, so 50 possible outcomes. Hence, n(S) = 50. Therefore, required probability, P(A) = n(A) / n(S) = 7/50.

Multiple choice

An urn contains 4 white and 2 red balls. Another urn contains 5 white and 3 red balls. One ball is drawn from each bag. The probability that both of them are white is

  1. 5/12

  2. 1/2

  3. 5/24

  4. 10/21

  5. 1/24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Probability of getting a white ball from first urn is, P(W1)=4/6 = 2/3. Probability of getting a white ball from second urn is, P(W2)= 5/8. Therefore, the required probability that both the balls are white is = 2/3 × 5/8 = 5/12.