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).

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