If the probabilities are 0.87, 0.36, and 0.29 that a family owns a color television set, a black television set, or both kind of sets: a. what is the probability that a family owns one or the other or both kind of sets? b. what is the probability that a family does not own any kind of set? c. what is the probability that a family owns only one kind of set?

Answer : (a) 0.94

              (b) 0.06

              (c) 0.58 and 0.07

Explanation :

We have given that

Event A : a family owns a color television set

Event B: a family owns a black television set

so,

Now, we have to calculate ,

=

And we know that ,

=

=

(c)

P(A)=family owns a color television set=0.87

P(B)=family owns a black television set=0.36

p(A  B)=family owns both kind of television set=0.29

(a) Probability that a family owns one or the other or both kind of sets=P(A B)= P(A) + P(B) - P(A  B)

=0.87+0.36-0.29

=1.23-0.29

0.94

(b) Probability that a family does not own any kind of set= 1 - P(A B )  =   1-0.94

       =0.06

(c) Probability that a family owns only one kind of set= P(A complement) + P(B complement)= P(A)- P(A  B) + P(B)- P(A  B)

=0.87-0.29+0.36-0.29

=0.58+0.07

=0.65