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A bank reports that families often have more than one credit card. The most popular in Australia are Mastercard, Visa and American Express. For those families with one or more of these cards, 30% have a Mastercard, 10% have an American Express card and 60% a Visa card. They also reported that 4% of families have both a Mastercard and an American Express card, 7% have both a Mastercard and a Visa card and only 3% have both a Visa card and an American Express card. Further, 1% have all three cards.
a. Calculate the probability of selecting a family that has either a Visa card or a Mastercard.
b. If a family has a Mastercard, what is the probability it also has a Visa card?
c. Is possession of a Mastercard independent of possession of a Visa card? Why or why not.
d. Is possession of an American Express card mutually exclusive of possession of a Visa card? Justify your decision.
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