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Chapter 3: Q. 3.25 (page 203)

In a standard deck, there are 52cards. Twelve cards are face cards (F) and 40cards are not face cards (N). Draw two cards, one at a time, without replacement. The tree diagram is labeled with all possible probabilities.

a. Find P(FN OR NF).

b. Find P(NF).

c. Find P (at most one face card).

Hint: "At most one face card" means zero or one face card.

d. Find P (at least on face card).

Hint: "At least one face card" means one or two face cards.

Short Answer

Expert verified

a. The value of P(F N O R N F) is 0.362.

b. The value of P(N F) is 0.784.

c. The value of P (at most one face card) is 0.950.

d. The value of P (at least on face card) is 0.412.

Step by step solution

01

Introduction

Number of cards in a deck =52

face cards =12 and non face cards =40

02

Explanation (Part a)

We have a tree diagram.

As a result, the needed probability can be computed as follows:

P(FNORNF)=P(FN)+P(NF)=4802562+4802562=0.362

03

Explanation (Part b)

We have a tree diagram.

As a result, the needed probability can be computed as follows:

P(N鈭�F)=4051=0.784

04

Explanation (Part c)

We have a tree diagram.

As a result, the needed probability can be computed as follows:

P(at most one face card)=P(FN)+P(NF)+P(NN)=4802652+4802652+15602652=0.950

05

Explanation (Part d)

We have a tree diagram.

As a result, the needed probability can be computed as follows:

P(at least one face card)=P(FF)+P(FN)+P(NF)=1322652+4802652+4802652=0.412

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