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Chapter 3: Q. 119 (page 231)

Given events G and H: P(G) = 0.43; P(H) = 0.26; P(H AND G) = 0.14

a. Find P(H OR G).

b. Find the probability of the complement of event (H AND G).

c. Find the probability of the complement of event (H OR G).

Short Answer

Expert verified

a. P(HORG)=0.55

b.role="math" localid="1650389369124" P((HANDG)')=0.86

c.P((HORG)')=0.45

Step by step solution

01

Given information

Given events G and H: P(G) = 0.43; P(H) = 0.26; P(H AND G) = 0.14

02

Explanation (part a)

P(HORG)=P(H)+P(G)-P(HANDG)P(HORG)=0.43+0.26-0.14P(HORG)=0.55

03

Explanation (part b)

the probability of the complement of event (H AND G):

P((HANDG)')=1-P(HANDG)P((HANDG)')=1-0.14P((HANDG)')=0.86

04

Explanation (part c)

probability of the complement of event (H OR G):

P((HORG)')=1-P(HORG)

We know that P(HORG)=0.55

Therefore

P((HORG)')=1-0.55=0.45

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