A single card is drawn at random from a well-shuffled deck of 52 playing cards. Let
A be the event “the card drawn is a heart” and B be the event “the card drawn is an ace.”
a. (i) Find P(A) and P(B).
b. (ii) Find P(A∩B), the probability that the card drawn is both a heart and an ace.
c. (iii) Verify whether A and B are independent by comparing P(A∩B) with P(A)P(B).
d. (iv) Decide, with reason, whether A and B are mutually exclusive.