Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard. Suppose that P (A) = 0.6, P (B) = 0.5, and P (A n B) = 0.15.

(a) Compute the probability that the selected individual has at least one of the two types of cards (i. e., the probability of the event A? B).

(b) What is the probability that the selected individual has neither type of card?

c) Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard.

A' n B

A' n B'

A'? B'

A? B'

A n B'

Calculate the probability of this event.

a) 0.95

b) 0.05

c) (A∩B')

0.45

Step-by-step explanation:

We know that P (A) = 0.6, P (B) = 0.5 and P (A∩B) = 0.15.

a)

P (At least one of two types of cards) = P (A∪B) = ?

P (A∪B) = P (A) + P (B) - P (A∩B) = 0.6+0.5-0.15=0.95

Thus, the probability that the selected individual has at least one of the two types of cards is 0.95.

b)

P (neither type of card) = P[ (A∪B) ']

P[ (A∪B) ']=1-P (A∪B) = 1-0.95=0.05

Thus, the probability that the selected individual has neither type of card is 0.05.

c)

As event A denote that selected individual has a Visa card and event B denote that selected individual has a Master card, so the event that the selected student has a visa card but not a Master card can be denoted as (A∩B').

P (A∩B') = P (A) - P (A∩B) = 0.6-0.15=0.45

Thus, the probability that the selected student has a Visa card but not a MasterCard is 0.45.