The student club Has IPhone or HIP requires all the members

The student club “Has I-Phone” or HIP requires all the members to have I-Phones. Currently 50% have the I-Phone 6 (A), 30% the I-Phone 5 (B) and 10% have both of these IPhones. A HIP member is randomly selected. Answer the following question and draw Venn diagram(s) to support your answer.

a.   What is the probability that the selected member has at least one of these two phones?

b.   What is the probability that the selected member has neither of these two phones?

c.   What is the probability that the selected member has only an I-Phone 6?

d.   What is the probability that the selected member has only one of these two phones?

Solution

A : Event that the member selected has an I-phone 6(A)

B : Event that the member selected has an I-phone 5(B)

P(A ) = 0.50 ; P(B) = 0.30 ; P( A and B) = 0.1

a.) P( at least one of the two phones)

= P( A U B)

= P(A) + P(B) - P( A and B)

= 0.5 + 0.3 -0.1

= 0.7

b.) P(neither of the two phones)

= 1 - P( at least one of the two phones)

= 1 - 0.7 = 0.3

c.) P( only an I phone 6) = 0.5 - 0.1 = 0.4

d.) (Only one of these two phones)

= 0.5 + 0.3

= 0.8