2 7 - 3 2 Conditional Probability These exercises involve conditional probability.

A card is drawn from a deck. Find the following conditional probability.

(a) The card is queen, given that it is a face card.

(b) The card is a king, given that it is a spade.

(c) The card is a spade, given that it is a king.

(a)

To find:

The conditional probability that the drawn card is a queen, given that it is a face card.

Given:

A card is drawn from a deck.

Approach:

p(A|B)=p(A∩B)p(B) …(1)

Here, p(A|B) is the conditional probability of an event A given that B has already occurred, p(A∩B) is the joint probability of events A and B, p(B) is the probability of event B.

There are 4 suits in a deck of 52 playing cards, each of the four suits, spades, diamonds, hearts, and clubs, contain 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

Jack, Queen, King are face cards, there are total 12 face cards.

Calculation:

Suppose E is the event that the drawn card is a queen and F is the event that the drawn card is a face card.

p(E)=452

Here, p(E) is the probability of a queen in a deck of 52 playing cards.

p(F)=1252

Here, p(F) is the probability of face card in a deck of 52 playing cards

(b)

To find:

The conditional probability that the drawn card is a king, given that it is a spade.

(c)

To find:

The conditional probability that the drawn card is a spade, given that it is a king.