Chapter 8.6, Problem 34E

To determine

To find: the probability of the union of the two events (the card is a face card or a black card) using the formula.

Answer to Problem 34E

The probability of the card is a face card or a black card $=\frac{8}{13}.$

Explanation of Solution

Given information: One card is selected at random from a standard deck of 52 playing

cards. The given two events are the card is a face card or a black card.

Formula Used.

If an event has n(E) equally likely outcomes and its sample space S has n(S) equally likely outcomes, then the probability of event is given by,

  $P(E)=\frac{n(E)}{n(S)}.$

If A and B are events in the same sample space, then the probability of A or B occurring is given by

  $P(A\cup A)=P(A)+P(B).$

Calculation:

The total number of cards from a standard deck =52.

There are two black suits and 13 cards in each suit, so the number of black cards=26.

The three face cards (J,Q,K) from the non-black suits (hearts and diamond) which gives the number of face cards from two non-black suits=6.

So, the probability of the card is a face card or a black card= $\frac{26}{52}+\frac{6}{52}=\frac{32}{52}=\frac{8}{13}.$