Exercise 26 Page 930

We are told that a card is randomly pulled from a standard deck. Recall that the experimental probability of an event measures the likelihood that the event occurs based on the actual results of an experiment. P=Times the Event Occurs/Times the Experiment Is Done We want to find the probability of selecting a card that is not a face card. Note that this is the complement of selecting a card that is a face card. The sum of the probability of an event and the probability of its complement is 1. P(Event)+P(Not event)=1

Let's start by finding the probability of selecting a face card, which will be our event. There are 52 cards in a deck, which is also the number of times the experiment is done.

In the deck, there is a total of 3 club face cards, 3 diamond face cards, 3 spade face cards, and 3 heart face cards. The sum of these values is the number of times the event occurs. 3+3+3+3= 12 face cards Now we have enough information to calculate P(Face card).

P=Times the Event Occurs/Times the Experiment Is Done

SubstituteValues

Substitute values

P(Face card)=12/52

ReduceFrac

a/b=.a /4./.b /4.

P(Face card)=3/13

The experimental probability of selecting a face card is 313. Let's now find the probability of its complement, which is selecting a card that is not a face card.

P(Face card)+P(Not a face card)=1

Substitute

P(Face card)= 3/13

3/13+P(Not a face card)=1

▼

Solve for P(Not a face card)

SubEqn

LHS-3/13=RHS-3/13

P(Not a face card)=1-3/13

OneToFrac

Rewrite 1 as 13/13

P(Not a face card)=13/13-3/13

SubFrac

Subtract fractions

P(Not a face card)=10/13

▼

Convert to percent

CalcQuot

Calculate quotient

P(Not a face card)=0.769231...

RoundDec

Round to 3 decimal place(s)

P(Not a face card)≈0.769

WritePercent

Convert to percent

P(Not a face card)≈76.9 %

We found that P(Not a face card) is equal to 1013 or about 76.9 %.