Question

Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose that P(A) = 0.6 and P(B) = 0.3.

a. What is the probability that the selected student has neither type of card?b. Describe in terms of A and B the event that the select student has a visa card, but not a mastercard? and then calulate the probability of this event.c. Calcuate th probability that the selected student has exactly one of the two types of cards?

Answer 1

a) Therefore, the probability is P=0.28.

b) Therefore, the probability is P=0.42.

c) Therefore, the probability is P=0.54.

Explanation:

We know that A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose that:

P(A) = 0.6 and P(B) = 0.3.

a) We calculate the probability that the selected student has neither type of card:

`P=1-P(A\cup B)\\\\P=1-P(P(A)\cup P(B)\cap P(A\cap B))\\\\P=1-(0.6+0.3-P(A)P(B))\\\\P=1-(0.9-0.6\cdot 0.3)\\\\P=1-(0.9-0.18)\\\\P=1-0.72\\\\P=0.28`

Therefore, the probability is P=0.28.

b) We calculate the probability that the select student has a visa card, but not a mastercard:

`P=P(A)-P(A\cap B)\\\\P=0.6-P(A)P(B)\\\\P=0.6-0.6\cdot 0.3\\\\P=0.6-0.18\\\\P=0.42`

Therefore, the probability is P=0.42.

c) We calculate the probability that the selected student has exactly one of the two types of cards:

`P=[P(A)-P(A\cap B)]+[P(B)-P(A\cap B)]\\\\P=[0.6-0.18]+[0.3-0.18]\\\\P=0.42+0.12\\\\P=0.54`

Therefore, the probability is P=0.54.