A standard deck of cards has 52 cards. You choose one card from the deck. Let event A be you choose a black card and event B be you choose a king. Find P(A)⋅P(B) , P(A and B) , and determine whether events A and B are independent.Enter the first two answers in fraction form.

Question

A standard deck of cards has 52 cards. You choose one card from the deck. Let event A be you choose a black card and event B be you choose a king. Find P(A)⋅P(B) , P(A and B) , and determine whether events A and B are independent.Enter the first two answers in fraction form.

Answer 1

There are 26 black cards and 4 kings in a standard deck of 52 cards.

P(A) = number of black cards / total number of cards = 26/52 = 1/2
P(B) = number of kings / total number of cards = 4/52 = 1/13

P(A) * P(B) = (1/2) * (1/13) = 1/26

There are 2 black kings in the deck, so
P(A and B) = number of black kings / total number of cards = 2/52 = 1/26

Since P(A and B) = P(A) * P(B), events A and B are independent.