Question

4. Consider an experiment with a standard 52-deck from which one card is randomly selected and not replaced. Then a second card is randomly selected. Define the following events Event A The first card is a heart Event B The second card is a heart Are these two events mutually exclusive? Why or Why not? Are these two events independent? Why or why not? (20 points) a. b.

Answer 1

a) The two events are not mutually exclusive.

Two events are called mutually exclusive events when those two events cannot occur at the same time. Here, it is possible that both first card and second card are hearts. So, the events are not mutually exclusive.

b) Number of hearts = 13

Number of cards = 52

P(A) = 13/52

P(B) = 13/52

P(B | A) = 12/52

If two events A and B are independent, P(B) = P(B | A)

Here, P(B) $\neq$ P(B | A)

Therefore, the events are not independent