You have a standard deck of cards. The deck has 525252 total cards and contains 444 suits: hearts, clubs, diamonds, and spades. Each suit consists of cards numbered 2-102−102, minus, 10, a jack, a queen, a king, and an ace.
You select one card at random from the deck. Let AAA be the event that the randomly selected card is a diamond and let BBB be the event that the card is a king. Based on this information, answer the following questions.
What is P(A)P(A)P, left parenthesis, A, right parenthesis, the probability that the card is a diamond?
What is P(B)P(B)P, left parenthesis, B, right parenthesis, the probability that the card is a king?
What is P(A\text{ and }B)P(A and B)P, left parenthesis, A, start text, space, a, n, d, space, end text, B, right parenthesis, the probability that the card is a diamond and a king?
What is P(A\text{ | }B)P(A | B)P, left parenthesis, A, start text, space, vertical bar, space, end text, B, right parenthesis, the conditional probability that the card is a diamond given that it is a king?
Is P(A\text{ | }B)=P(A)P(A | B)=P(A)P, left parenthesis, A, start text, space, vertical bar, space, end text, B, right parenthesis, equals, P, left parenthesis, A, right parenthesis? Are the events AAA and BBB independent?
Choose all answers that apply:
Choose all answers that apply:
