Given that an individual is selected at random and that he o

Given that an individual is selected at random and that he or she has at least one card, what is the probability that he or she has a Visa card? (write your answer in four decimal places)

Solution

Note that

P(has card) = P(visa) + P(master) - P(visa and master)

Thus,

P(has card) = 0.5 + 0.4 - 0.25 = 0.65.

Also, note that

P(visa|has card) = P(visa and has card)/P(has card)

As P(visa) is just a subset of P(has card),

P(visa and has card) = P(visa)

Thus,

P(visa|has card) = P(visa)/P(has card)

P(visa|has card) = 0.5/0.65 = 0.7692 [ANSWER]