A standard deck of cards has 52 cards. The 52 cards are divided into four suits: diamonds, clubs, hearts, and spades. Diamonds and hearts are red cards, and clubs and spades are black cards. Suppose you choose a card from the deck. Let event A be you choose a red card and event B you choose an ace. Determine P(A∩B)

Question

A standard deck of cards has 52 cards. The 52 cards are divided into four suits: diamonds, clubs, hearts, and spades. Diamonds and hearts are red cards, and clubs and spades are black cards. Suppose you choose a card from the deck. Let event A be you choose a red card and event B you choose an ace. Determine P(A∩B)

, P(A)
, and P(B)
, and state whether events A and B are independent.

Enter the first three answers in fraction form. Reduce your answer.

(4 points)
P(A∩B)=

P(A)=

P(B)=

Enter 1 is events A and B are dependent. Enter 2 if events A and B are independent.

Answer 1

P(A∩B) = 2/52 = 1/26

P(A) = 26/52 = 1/2

P(B) = 4/52 = 1/13

Events A and B are independent, as P(A)∩P(B) = P(A)*P(B).

Therefore, events A and B are independent.