Mathematics

Probability

337 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 box contains 10 defective items and 90 non-defective items. If two items are randomly selected without replacement, what is the probability that both items are defective?

  1. 1/100

  2. 1/50

  3. 1/25

  4. 1/10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The probability of selecting a defective item on the first draw is 10/100. After the first draw, there are 9 defective items and 89 non-defective items remaining. The probability of selecting a defective item on the second draw is 9/99. Therefore, the probability of selecting two defective items is (10/100) * (9/99) = 1/100.

Multiple choice

A survey found that 60% of people prefer coffee, 30% prefer tea, and 10% prefer both coffee and tea. What is the probability that a randomly selected person prefers coffee or tea?

  1. 0.8

  2. 0.9

  3. 0.7

  4. 0.6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The probability of preferring coffee or tea is the sum of the probabilities of preferring coffee and preferring tea, minus the probability of preferring both. So, P(coffee or tea) = P(coffee) + P(tea) - P(coffee and tea) = 0.6 + 0.3 - 0.1 = 0.9.

Multiple choice

A bag contains 4 red balls, 3 blue balls, and 2 green balls. If two balls are randomly selected without replacement, what is the probability that the first ball is red and the second ball is blue?

  1. 3/14

  2. 6/35

  3. 2/21

  4. 1/10
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

The probability of selecting a red ball on the first draw is 4/9. After the first draw, there are 3 red balls, 3 blue balls, and 2 green balls remaining. The probability of selecting a blue ball on the second draw is 3/8. Therefore, the probability of selecting a red ball on the first draw and a blue ball on the second draw is (4/9) * (3/8) = 3/35.

Multiple choice

A fair six-sided die is rolled twice. What is the probability of getting a sum of 7?

  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 a fair six-sided die twice. 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

A survey found that 40% of people prefer coffee, 30% prefer tea, and 20% prefer both coffee and tea. What is the probability that a randomly selected person prefers only coffee?

  1. 0.2

  2. 0.3

  3. 0.4

  4. 0.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The probability of preferring only coffee is the probability of preferring coffee minus the probability of preferring both coffee and tea. So, P(coffee only) = P(coffee) - P(coffee and tea) = 0.4 - 0.2 = 0.2.

Multiple choice

A random variable X has a probability mass function given by P(X = x) = 1/6 for x = 1, 2, 3, 4, 5, 6. Find the expected value of X.

  1. 3.5

  2. 4

  3. 4.5

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

The expected value of X is given by E(X) = Σ[x * P(X = x)] for all possible values of X. So, E(X) = 1 * (1/6) + 2 * (1/6) + 3 * (1/6) + 4 * (1/6) + 5 * (1/6) + 6 * (1/6) = 3.5.

Multiple choice

What is the probability of selecting a specific element from a population of size N using simple random sampling?

  1. 1/N

  2. N/1

  3. 1/(N-1)

  4. (N-1)/N
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In simple random sampling, each element in the population has an equal chance of being selected, so the probability of selecting a specific element is 1/N.

Multiple choice

What is the probability of getting a head when you flip a coin?

  1. 1/2

  2. 1/4

  3. 1/3

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

When you flip a coin, there are two possible outcomes: heads or tails. 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 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.