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Chapter 3: Q35E (page 180)

The outcomes of two variables are (Low, Medium, High) and (On, Off), respectively. An experiment is conducted in which the outcomes of each of the two variables are observed. The accompanying two-way table gives the probabilities associated with each of the six possible outcome pairs.

Low

Medium

High

On

.50

.10

.05

Off

.25

.07

.03

Consider the following events:

A: {On}

B: {Medium or on}

C: {Off and Low}

D: {High}

a. Find P (A).

b. Find P (B).

c. Find P (C).

d. Find P (D).

e. FindP(AC).

f. FindP(A鈭�B).

g. FindP(A鈭�B).

h. Consider each pair of events (A and B, A and C, A and D, B and C, B and D, C and D). List the pairs of events that are mutually exclusive. Justify your choices.

Short Answer

Expert verified
  1. 0.65
  2. 0.72
  3. 0.25
  4. 0.08
  5. 0.35
  6. 0.72
  7. 0
  8. A and C, A and D, B and D, & C and D.

Step by step solution

01

Introduction

Probability is organizing trials and comparing the number of possible outcomes to the number of desired outcomes.

02

Find P (A)

P(A)=[0.50+0.10+0.05]=0.65

03

Find P (B)

P(B)=P(on)+P(medium)-P(medium鈭�low)=[(0.10+0.7)+(0.50+0.10+0.05)鈭�0.10]=[0.17+0.65鈭�0.10]=0.72

04

Find P (C)

P(C)=0.25

05

Find P (D)

P(D)=[0.05+0.03]=0.08

06

Find P(Ac)

P(Ac)=1鈭�P(A)=1鈭�0.65=0.35

07

Find

P(A鈭�B)=P[Onor(mediumorOn)]=P(Onormedium)=P(B)=0.72

08

Find

P(A鈭�C)=P[Onand(OffandLow)

Here, On & Off and Low are mutually exclusive.

P(A鈭�C)=0

09

List all the mutually exclusive pairs

P(A鈭�C)=0

P(A鈭�D)=0

P(B鈭�C)=0

P(C鈭�D)=0

Therefore,A and C, A and D, B and D, & C and Dare mutually exclusive pairs.

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