Consider randomly selecting a student at a certain university, and let A denote

Question

Consider randomly selecting a student at a certain university, and let A denote the event that the selected student has a Visa credit card and let B denote the event that the student has a MasterCard. Suppose that P (A )=.6, and P (B )=.4  . For this part of the question, assume P (A B )= .3 .

Describe in terms of A and B the event that the selected student has a Visa Card but not a Mastercard. That is, use one or more of the operation (write cap), (write cup), (or just ') and/or set minus (-). There are several equivalent formulas.?

Compute the probability that the selected student has a Visa Card but not a Mastercard.?

Compute the probability that the selected student has a exactly one of the two types of cards.?

Explanation / Answer

P(A) =.6, and P(B) =.4 P(A B) = .3

The event that a selected student has a Visa Card but not a Mastercard is P(A - B).

The probability that the selected student has a Visa Card but not a Mastercard = P(A - B) = P(A) - P(A B) = .6 - .3 = .3

The probability that the selected student has a Mastercard but not a Visa Card = P(B - A) = P(B) - P(A B) = .4 - .3 = .1

The probability that the selected student has a exactly one of the two types of cards = P(A - B) + P(B - A)

= .3 + .1 = .4

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