Question

In a certain city, 27% of the families have a MasterCard, 19% have an American Express card, and 22% have a Visa card. Nine percent of the families have both a MasterCard and an American Express card. Fourteen percent have both a Visa card and a MasterCard. Six percent have both an American Express card and a Visa card. What is the probability of selecting a family that has either a Visa card or an American Express card?

Answer 1

35%

Explanation:

Data provided in the question:

P(Master card) = 27% = 0.27

P(American express card) = 19% = 0.19

P( Visa card ) = 22% = 0.22

P( Master and American express card ) = 9% = 0.09

P( Visa and master card ) = 14% = 0.14

P( American express and visa card ) = 6% = 0.06

Now,

The probability of selecting a family that has either a Visa card or an American Express card

= P( Visa card ) + P( American express card ) - P( Visa and American express card )

= 0.22 + 0.19 - 0.06

= 0.35

or

= 0.35 × 100% = 35%