Question

Of 10,000 students at a university, 2,500 have a MasterCard card (M), 4,000 have a Visa card (V), and 4,000 have neither card.

A. Find the probability that a randomly selected student has both cards?

B. Find the probability that a randomly selected student has at least one of these two cards?

C. Find the probability that a randomly selected student has a MasterCard but not a Visa card?

D. [What proportion of students who have a MasterCard also have a Visa card?

Answer 1

P(V) = 4000/10,000 = 0.4

P(M) = 2500/10,000 = 0.25

P(M' V') = 4000/10,000 = 0.4

P(M U V) = 1 - P(M' V')

= 1 - 0.4

= 0.6

A. P(both cards) = P(M V) = P(M) + P(V) - P(M U V)

= 0.25 + 0.4 - 0.6

= 0.05

B. P(at least one of the two cards), P(M U V) = 0.6

C. P(MasterCard but not Visa card) = P(M) - P(M V)

= 0.25 - 0.05

= 0.20

D. P(Visa card | MasterCard), P(V | M) = P(V M)/P(M)

= 0.05/0.25

= 0.20