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 or 11 when rolling two fair six-sided dice?

  1. 1/4

  2. 1/6

  3. 1/8

  4. 1/12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are 36 possible outcomes when rolling two six-sided dice. The outcomes that sum to 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). The outcomes that sum to 11 are (5, 6), (6, 5). Therefore, the probability of getting a sum of 7 or 11 is (6 + 2)/36 = 8/36, which simplifies to 1/6.

Multiple choice

What is the probability of getting a sum of 2, 3, or 12 when rolling two fair six-sided dice?

  1. 1/9

  2. 1/6

  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 six-sided dice. The outcomes that sum to 2 are (1, 1). The outcomes that sum to 3 are (1, 2), (2, 1). The outcomes that sum to 12 are (6, 6). Therefore, the probability of getting a sum of 2, 3, or 12 is (1 + 2 + 1)/36 = 4/36, which simplifies to 1/9.

Multiple choice

What is the probability of getting a sum of 4, 5, 6, 7, 8, 9, 10, or 11 when rolling two fair six-sided dice?

  1. 1/2

  2. 2/3

  3. 3/4

  4. 5/6
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

There are 36 possible outcomes when rolling two six-sided dice. The outcomes that sum to 4 are (1, 3), (2, 2), (3, 1). The outcomes that sum to 5 are (1, 4), (2, 3), (3, 2), (4, 1). The outcomes that sum to 6 are (1, 5), (2, 4), (3, 3), (4, 2), (5, 1). The outcomes that sum to 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). The outcomes that sum to 8 are (2, 6), (3, 5), (4, 4), (5, 3), (6, 2). The outcomes that sum to 9 are (3, 6), (4, 5), (5, 4), (6, 3). The outcomes that sum to 10 are (4, 6), (5, 5), (6, 4). The outcomes that sum to 11 are (5, 6), (6, 5). Therefore, the probability of getting a sum of 4, 5, 6, 7, 8, 9, 10, or 11 is (3 + 4 + 5 + 6 + 5 + 4 + 3 + 2)/36 = 32/36, which simplifies to 5/6.

Multiple choice

What is the probability of getting a sum of 13 or more when rolling two fair six-sided dice?

  1. 0

  2. 1/6

  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 six-sided dice. The highest possible sum is 12. Therefore, the probability of getting a sum of 13 or more is 0.

Multiple choice

What is the probability of getting a sum of 1 or 13 when rolling two fair six-sided dice?

  1. 1/18

  2. 1/12

  3. 1/9

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

There are 36 possible outcomes when rolling two six-sided dice. The outcomes that sum to 1 are (1, 1). The outcomes that sum to 13 are (6, 6). Therefore, the probability of getting a sum of 1 or 13 is (1 + 1)/36 = 2/36, which simplifies to 1/18.

Multiple choice

What is the probability of getting a sum of 2 or 12 when rolling two fair six-sided dice?

  1. 1/9

  2. 1/6

  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 six-sided dice. The outcomes that sum to 2 are (1, 1). The outcomes that sum to 12 are (6, 6). Therefore, the probability of getting a sum of 2 or 12 is (1 + 1)/36 = 2/36, which simplifies to 1/18.

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 the coin is fair, each outcome is equally likely to occur. Therefore, the probability of getting a head is 1/2.

Multiple choice

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

  1. 1/6

  2. 1/12

  3. 1/18

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

When two fair dice are rolled, there are 36 possible outcomes. The outcomes that result in a sum of 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 expected value of the sum of two fair dice?

  1. 7

  2. 8

  3. 9

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

The expected value of a random variable X is given by the formula E(X) = ΣxP(X = x), where x is the value of the random variable and P(X = x) is the probability of X taking the value x. In this case, the random variable X is the sum of two fair dice. The possible values of X are 2, 3, 4, ..., 12. The probability of getting each value is 1/36. Therefore, the expected value of X is E(X) = 2(1/36) + 3(1/36) + 4(1/36) + ... + 12(1/36) = 7.

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

For a fair coin, the probability of getting a head or a tail is equal, hence the probability of getting a head is 1/2.

Multiple choice

What is the probability of getting at least one head when flipping two fair coins?

  1. 1/4

  2. 1/2

  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 is the complement of the probability of getting no heads. The probability of getting no heads is (1/2) * (1/2) = 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 a sum of 7 when rolling two fair six-sided dice?

  1. 1/6

  2. 1/12

  3. 1/18

  4. 1/36
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

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

The probability of getting a head when flipping a fair coin is 1/2.

Multiple choice

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

  1. 1/6

  2. 1/12

  3. 1/18

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

The probability of getting a sum of 7 when rolling two fair dice is 1/6.

Multiple choice

What is the probability of getting a sum of 11 when rolling two fair dice?

  1. 1/6

  2. 1/12

  3. 1/18

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

The probability of getting a sum of 11 when rolling two fair dice is 1/18.