Question

You have a standard deck of cards. The deck has 52 total cards and contains 4 suits: hearts, clubs, diamonds, and spades. Each suit consists of cards numbered 2-10, a jack, a queen, a king, and an ace.
You select one card at random from the deck. Let A be the event that the randomly selected card is a diamond and let B be the event that the card is a king. Based on this information, answer the following questions.

1)What is P(A|B), the conditional probability that the card is a diamond given that it is a king?

2)Are the events A and B independent?

Answer 1

Answer:

1) ¼

2) yes

Step-by-step explanation:

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

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

P(A^B) = 1/52

P(A|B) = (1/52) ÷ (1/13) = 1/4

Since P(A|B) = P(A), they are independent