Probability and Distributions Flashcards

If P(B|A) = 0.6 and P(A) = 0.5, what is P(A ∩ B)?

Answer: 0.30

By the multiplication rule, P(A ∩ B) = P(B|A) × P(A) = 0.6 × 0.5 = 0.30.

For a symmetric, bell-shaped distribution with mean 70 and median 70, if a value has z = 2.0, it is:

Answer: Above the mean by 2 standard deviations

A positive z-score of 2.0 indicates the value is 2 standard deviations above the mean.

Which condition must be met for the binomial model to apply?

Answer: Fixed number of trials, each with two outcomes and constant probability of success

Binomial requires: fixed n, binary outcomes (success/failure), constant p, and independent trials.

A continuous random variable has pdf f(x) = 2x for 0 ≤ x ≤ 1. What is P(X ≤ 0.5)?

Answer: 0.25

P(X ≤ 0.5) = ∫₀^0.5 2x dx = [x²]₀^0.5 = 0.25.

The complement rule states that for any event A:

Answer: P(Aᶜ) = 1 − P(A)

Since A and Aᶜ partition the sample space, P(A) + P(Aᶜ) = 1, so P(Aᶜ) = 1 − P(A).

For a normal distribution, what is the area to the LEFT of z = 1.96?

Answer: 0.9750

From the standard normal table, P(Z < 1.96) = 0.9750, leaving 0.025 in each tail for a 95% interval.

Which of the following describes a discrete probability distribution?

Answer: The number of heads in 10 coin flips

The number of heads is countable (0, 1, 2, …, 10), making it a discrete random variable.