Probability

Q. How many ways can you choose 2 items from a set of 5?

Solution

The number of ways to choose 2 items from 5 is calculated using combinations: C(5,2) = 5! / (2!(5-2)!) = 10.

Correct Answer: A — 10

Q. If a die is rolled, what is the probability of rolling an even number?

Solution

There are 3 even numbers (2, 4, 6) out of 6 possible outcomes, so the probability is 3/6 = 1/2.

Correct Answer: A — 1/2

Q. If two coins are flipped, what is the probability of getting at least one head?

Solution

The only outcome without a head is TT, so the probability of at least one head is 3/4.

Correct Answer: C — 3/4

Q. In a binomial distribution, what is the probability of getting exactly 3 successes in 5 trials with a success probability of 0.5?

Solution

Using the binomial formula: P(X=3) = C(5,3) * (0.5)^3 * (0.5)^(5-3) = 10 * 0.125 * 0.25 = 0.3125.

Correct Answer: B — 0.3125

Q. What is the mean of the following data set: 2, 4, 6, 8, 10?

Solution

Mean = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.

Correct Answer: C — 6

Q. What is the median of the following data set: 3, 1, 4, 2, 5?

Solution

First, sort the data: 1, 2, 3, 4, 5. The median is the middle value, which is 3.

Correct Answer: B — 3

Q. What is the mode of the following data set: 1, 2, 2, 3, 4?

Solution

The mode is the number that appears most frequently, which is 2.

Correct Answer: B — 2

Q. What is the standard deviation of the data set: 4, 8, 6, 5, 3?

Solution

Mean = 5.2; Variance = 2.5; Standard deviation = √2.5 ≈ 1.58.

Correct Answer: B — 2.24

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