MCQ Subject: Probability & Statistics

If two independent events A and B have probabilities P(A) = 0.4 and P(B) = 0.5, what is the probability that both A and B occur?

Two fair dice are rolled independently. Given that the sum of the dice is 7, what is the probability that at least one die shows a 4?

Which distribution ensures that the sampling distribution of the mean is identical to the population distribution for any sample size?

A card is drawn from a standard deck of 52 cards. Given that the card drawn is a King, what is the probability it is the King of Spades?

Given events A and B with probabilities P(A) = 0.3, P(B) = 0.6, and P(A ∪ B) = 0.75, what is P(A|B) if P(A ∩ B) = 0.18?

Given events A and B where P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.2, what is P(A|B)?

Two events A and B have probabilities P(A) = 0.4 and P(B) = 0.5. If the probability of both A and B occurring is P(A ∩ B) = 0.2, what is the probability of A given B has occurred, P(A|B)?