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

What is the probability of getting a sum of 7 when you roll two dice?

  1. 1/6

  2. 1/12

  3. 1/18

  4. 1/24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are 36 possible outcomes when you roll two dice. The outcomes that sum to 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). So, the probability of getting a sum of 7 is 6/36 = 1/6.

Multiple choice

What is the probability of obtaining a head when flipping a fair coin?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since a fair coin has two equally likely outcomes (head or tail), the probability of obtaining a head is 1/2.

Multiple choice

What is the probability of getting a head when flipping a coin?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When flipping a coin, there are two possible outcomes: head or tail. Since each outcome is equally likely, the probability of getting a head is (1/2).

Multiple choice

What is the probability of getting two heads when flipping two coins?

  1. 1/4

  2. 1/2

  3. 3/4

  4. 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When flipping two coins, there are four possible outcomes: HH, HT, TH, and TT. Since each outcome is equally likely, the probability of getting two heads is (1/4).

Multiple choice

In a fair coin toss, what is the probability of getting heads?

  1. 1/2

  2. 1/4

  3. 1/3

  4. 1/6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a fair coin toss, there are two equally likely outcomes: heads or tails. Therefore, the probability of getting heads is 1/2.

Multiple choice

What is the probability of getting at least one head in two coin tosses?

  1. 1/2

  2. 1/4

  3. 3/4

  4. 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of getting at least one head in two coin tosses is the complement of the probability of getting no heads. The probability of getting no heads is (1/2)^2 = 1/4. Therefore, the probability of getting at least one head is 1 - 1/4 = 3/4.

Multiple choice

What is the probability of getting exactly two heads in three coin tosses?

  1. 1/2

  2. 1/4

  3. 3/8

  4. 1/8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of getting exactly two heads in three coin tosses is given by the binomial distribution with n = 3 and p = 1/2. The probability of getting exactly k heads in n coin tosses is given by P(X = k) = (n choose k)p^k(1-p)^(n-k). In this case, P(X = 2) = (3 choose 2)(1/2)^2(1/2)^1 = 3/8.

Multiple choice

What is the probability of getting a sum of 7 in a roll of two fair dice?

  1. 1/6

  2. 1/12

  3. 1/18

  4. 1/24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are 36 possible outcomes when rolling two fair dice. The outcomes that sum to 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). Therefore, the probability of getting a sum of 7 is 6/36 = 1/6.

Multiple choice

What is the probability of getting a head when flipping a fair coin?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A fair coin has two possible outcomes: head and tail. Since each outcome is equally likely, the probability of getting a head is 1/2.

Multiple choice

What is the probability of getting a sum of 7 when rolling two fair dice?

  1. 1/6

  2. 1/5

  3. 1/4

  4. 1/3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are 36 possible outcomes when rolling two dice. The outcomes that sum to 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). Therefore, the probability of getting a sum of 7 is 6/36 = 1/6.

Multiple choice

A bag contains 10 red balls, 15 blue balls, and 20 green balls. If a ball is randomly selected from the bag, what is the probability that it is a red ball?

  1. 1/5

  2. 2/5

  3. 3/5

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

There are a total of 10 + 15 + 20 = 45 balls in the bag. The probability of selecting a red ball is the number of red balls divided by the total number of balls, which is 10 / 45 = 1/5.

Multiple choice

What is the probability of getting a head when a fair coin is tossed?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When a fair coin is tossed, there are two possible outcomes: head or tail. Since each outcome is equally likely, the probability of getting a head is 1/2.

Multiple choice

A box contains 12 red balls, 8 blue balls, and 6 green balls. If a ball is randomly selected from the box, what is the probability of selecting a red ball?

  1. 1/2

  2. 1/3

  3. 2/5

  4. 3/8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find the probability of selecting a red ball, we divide the number of red balls by the total number of balls: 12 red balls / (12 red balls + 8 blue balls + 6 green balls) = 12/26 = 1/2.

Multiple choice

A box contains 15 red balls, 10 blue balls, and 5 green balls. If a ball is randomly selected from the box, what is the probability of selecting a blue ball?

  1. 1/3

  2. 1/4

  3. 1/5

  4. 1/6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find the probability of selecting a blue ball, we divide the number of blue balls by the total number of balls: 10 blue balls / (15 red balls + 10 blue balls + 5 green balls) = 10/30 = 1/3.

Multiple choice

What is the probability of getting a head when flipping a coin?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When flipping a coin, there are two possible outcomes: head or tail. Since both outcomes are equally likely, the probability of getting a head is 1/2.