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?

Question

Mathematics

Sydnee

17 April, 01:28

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?

+2

Answers (1)

Know the Answer?

Haylie Ibarra · Answer 1

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