Chapter 8.6, Problem 35E

To determine

To find: the probability of the union of the two events (the card is a 5 or a 2) using the formula.

Answer to Problem 35E

The probability of the card is a 5 or a 2 $=\frac{2}{13}.$

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 5 or a 2.

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.

The number of 5 cards=4.

The number of 2 cards=4.

So, the probability of the card is a 5 or a 2= $\frac{4}{52}+\frac{4}{52}=\frac{8}{52}=\frac{2}{13}.$