Question

Given events G and H: P(G) = 0.46; P(H) = 0.26; P(H AND G) = 0.13

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

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

Answer 1

We are given

P(G)=0.46

P(H)=0.26

P(H∩G)=0.13

(a)

we know that

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

=1-P(H∩G)

so, we can plug value

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

=1-0.13

=0.87.........Answer

(b)

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

=1-P(H∪G)

so, firstly we will find P(H∪G)

P(H∪G)=P(H)+P(G)-P(H∩G)

now, we can plug value

P(H∪G)=0.26+0.46-0.13

P(H∪G)=0.59

So,

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

=1-0.59

=0.41............Answer