Mathematics

Probability

303 Questions

Probability measures the likelihood of an event occurring, such as rolling a specific number on a die or drawing a colored ball. Questions cover simple events, mutually exclusive outcomes, and dice or coin combinations. This topic is consistently asked in mathematics and reasoning sections of competitive exams.

dice probabilitycoin toss eventsdrawing balls probabilitiesplaying card problemsmutually exclusive events

Probability Questions

Multiple choice

A bag contains 12 balls of two different colors, out of which x are white. One ball is drawn at random. If 6 more white balls areput in the bag, the probability of drawing a white ball now will be double that of the previous probability of drawing a white ball. Then, the value of x is _____.

  1. 3

  2. 4

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

1st Case x are white 12-x are non-white P(white) =x/12 2nd Casex+6 are white P(white)=(x+6)/18 According to question (x+6)/18= 2(x/12) Solve to get x=3

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 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

In a single throw of three dice, the probability of getting a total of 7 is

  1. 2/3

  2. 11/216

  3. 5/72

  4. 1/3

  5. 9/24
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total number of exhaustive cases = 6 × 6 × 6 = 216. Cases favourable to get a total of 7 is = 12 that is, (1,1,5); (1,2,4); (1,3,3); (1,4,2); (1,5,1); (2,1,4); (2,2,3); (2,3,2); (2,4,1); (3,1,3); (3,2,2); (3,3,1); ( 4,1,2); (4,2,1); (5,1,1). Hence, the required probability is = 15 /216 = 5/72.

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.

Multiple choice

A bag contains 5 analog watches and 3 digital watches. The second bag contains 7 analog watches and 4 digital watches. A watch when taken out from any bag. The probability that the watch being a digital watch is

  1. 3/88

  2. 61/154

  3. 65/88

  4. 65/176

  5. 29/70
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Probability of getting a digital watch out of the first bag is = 1/2 x 3/8 = 3/16. Probability of getting a digital watch out of the second bag is = 1/2 x 4/11 = 2/11. Both the two events are independent event. Therefore, required probability is, P = (1/2 x 3/8 + 1/2 x 4/11) = 65/ 176.

Multiple choice

Two tickets are drawn from 50 tickets numbered 1 to 50. The probability that their product being even is

  1. 12/49

  2. 2/49

  3. 37/98

  4. 2/7

  5. 37/49
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The product will be even if both or at least one ticket is even numbered. There are 25 even and 25 odd numbered tickets. Number of ways of selecting even numbered tickets = 25C2. Number of ways of selecting one even and one odd numbered ticket is = 25C1 × 25C1. From 50 tickets, 2 tickets can be drawn in 50C2 ways.Therefore, the required probability is = (25C2+25C1 × 25C1)/50C2 = 37/49.