A card is drawn at random from a standard deck of 52 cards. Find the following conditional probabilities. a) The card is a diamond, given that it is red. b) The card is red, given that it is a diamond. c) The card is a nine, given that it is red. d) The card is a king, given that it is a face card.

Step-by-step explanation:

P(A|B) = P(A and B) / P(B)

Total number of cards = 52

a)

Let A denotes the event that the card is a diamond and B denotes the card is red.

b)

Let A denotes the event that the card is red and B denotes the card is diamond.

c)

Let A denotes the event that the card is nine and B denotes the card is red.

d)

Let A denotes the event that the card is a king and B denotes the card is a face card.