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

There are 20 balls in a box out of which 4 are red, 9 are black and remaining are of some other colour. There is some probability of a red ball being selected in a random selection from the box. Which of the following actions will increase this probability?

  1. Put some more black balls in the box.

  2. Remove one red ball and 4 black balls from the box.

  3. Put one red ball and 4 black balls into the box.

  4. Remove some black balls from the box.

  5. Reduce some red balls from the box.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This will reduce the number of balls in the box but the number of red balls will remain same.

So, the probability of a red ball being selected will increase.

Multiple choice

In a box, there are 5 plastic balls and 10 wooden balls. Out of the 5 plastic balls, 3 are red and 2 are green. Similarly, the 10 wooden balls have 3 red and 7 green. What is the probability that a ball drawn from the box is either a plastic ball or red in color?

  1. 3/15

  2. 3/5

  3. 6/15

  4. 11/15

  5. 8/15
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The event of interest is; “the drawn ball should be either a plastic ball or red in color”. There are 5 plastic balls. Number of red balls is 6; 3 plastic and 3 wooden. Plastic red balls are already counted in 5 plastic balls. But the 3 wooden red balls should be added to get the number of balls that are either red or of plastic. Thus number of such balls is 5+3 = 8. Since, there are total 15 balls; required probability is 8/15.

Multiple choice

In a box of 30 balls, 10 balls are red and 20 green. Three balls have been drawn randomly from the box, in which 2 balls drawn are red and 1 ball is green. Now, another ball is drawn from the box without replacing already drawn balls. What change happens in the probability of a red ball being drawn compared to the same at the beginning?

  1. Does not change

  2. Insufficient data

  3. Decreases

  4. Increases

  5. Becomes half of the initial probability
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is correct, because more red balls have been drawn than green before the trial under question. This has reduced the percentage of red balls in the box.

Multiple choice

Six balls are drawn at random from a bag containing six white, five green and four black balls. The probability that exactly 3 of them are white is

  1. 16/143

  2. 48/143

  3. 12/143

  4. 32/143

  5. 4/1001
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

It is the correct answer. Solution- Total no of balls = 15No of ways of drawing 6 balls from 15 balls randomly=15C6 No of ways of drawing 3 white balls from 6 white balls = 6C3 No of ways of drawing other 3 balls from remaining 9 balls = 9C3 Required probability=(6C3 * 9C3) / 15C6 = 48/143

Multiple choice

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red is

  1. 2/91

  2. 89/91

  3. 4/91

  4. 1/3

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Probability of all the three balls being red  = 5C3/15C3                                                                              = 10/455                                                                              = 2/91 Hence, this option is correct.

Multiple choice

Two dice are thrown simultaneously. The probability of obtaining a total score of eight is

  1. 5/36

  2. 1/6

  3. 1/9

  4. 1/12

  5. 5/12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When two dice are thrown then there are 6 * 6 exhaustive cases. Therefore, n = 36.

Let A denote the event total score of 8 when 2 dice are thrown. Then A = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}

Thus, there are 5 favourable cases.

Therefore, m = 5

By definition P(A) = m/n = 5/36.

It is the correct answer.

Multiple choice

A bag contains 3 black and 6 white balls. Two draws of one ball each are made without replacement. What is the probability that one ball is black and the other is white?

  1. 2/9

  2. 1/2

  3. 1/4

  4. 4/9

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The given situation can be realised in two ways. First  ball is black and then 2nd  ball is white or first  ball is white and 2nd ball is black. So, p(E1) = probabilty of 1st  ball to be black p(E2) = probabilty of 1st ball to be white p(E3) = probabilty of 2nd  ball to be black p(E4) = probabilty of 2nd  ball to be white So, p(E) = p(E1)p(E4) + p(E2)*p(E3)                 = (1/3)(3/4)+(2/3)*(3/8) = 1/2

Multiple choice

A box contains 6 blue and 5 pink balls. Two balls are picked randomly one after the other from the box, without replacement. What is the probability that both balls are pink?

  1. 2/11

  2. 1/11

  3. 5/11

  4. 6/11

  5. 2/10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Probability of drawing a pink ball is 5/11. If the ball is not replaced, then the box will have one less pink ball, so the probability of drawing a pink ball in the next chance is 4/10. Hence, the probability of drawing 2 pink balls = 5/11 * 4/10 = 2/11. Hence, it is the correct answer.

Multiple choice

What is the probability of getting a prime number which is greater than or equal to five, when rolling a die?

  1. 2/6

  2. 1/6

  3. 1/2

  4. 4/6

  5. 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a die, there are only six numbers, i.e. 1, 2, 3, 4, 5, 6. A prime number is a number which can be divided by itself and 1. Now, find a prime number that is greater than or equal to 5, which is only number five. Hence, the probability will be 1/6. Hence, it is the correct answer.

Multiple choice

Which of the following are the various events of getting the sum of numbers as seven, when rolling a pair of dice?

  1. {(1, 6),(2, 5),(3, 4),(4, 3),(5, 2),(6, 0)}

  2. {(1, 6),(2, 5),(3, 4),(5, 2),(6, 1)}

  3. {(1, 6),(2, 5),(3, 4),(3, 3),(5, 2),(6, 1)}

  4. {(1, 6),(2, 5),(3, 4),(4, 3),(5, 2),(6, 1)}

  5. {(1, 6),(2, 5),(3, 4),(4, 3),(5, 2)}
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

It is the correct answer. In a die, there are only six numbers – 1, 2, 3, 4, 5, and 6. Various events of getting sum of dice as seven when rolling a pair of dice will be as follows: {(1, 6),(2, 5),(3, 4),(4, 3),(5, 2),(6, 1)}

Multiple choice

A bag contains 4 yellow balls, 5 green balls and 3 red balls. What will be the probability of getting red and yellow balls?

  1. 7/12

  2. 1/12

  3. 5/12

  4. 8/12

  5. 9/12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a bag, there are total 12 (5 + 4 + 3) balls. For getting 3 red balls, the probability is 3/12 and for getting 4 yellow balls, the probability is 4/12. Hence, the probability of getting red and green balls by using the product principle, is (3/12) * (4/12) = 1/12.

Multiple choice

A bag contains 5 yellow balls, 4 green balls and 3 red balls. What will be the probability of getting either a red ball or a green ball?

  1. 1/12

  2. 7/12

  3. 3/12

  4. 4/12

  5. 12/12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a bag, there are total 12 (5 + 4 + 3) balls. For getting 3 red balls, the probability is 3/12 and for getting 4 green balls, the probability is 4/12. Hence, getting either a red ball or a green ball by addition principle, the probability will be (3/12) + (4/12) = 7/12. Hence, it is the correct answer.