The following contingency table summarizes the number of students at a college w

Question

The following contingency table summarizes the number of students at a college who have a Mastercard or a Visa credit card.

Have Do Not Have
Visa Visa Total Total

Have 1,000 1,500 2,500
Mastercard  

Do not have
Mastercard 3,000 4,500 7,500

Total 4,000 6,000 10,000

a   Find the probability that a randomly selected student (1)   Has a Mastercard. (2)   Has a VISA. (3)   Has both credit cards

b   Find the probability that a randomly selected student
(1) Has a Mastercard or a VISA. (2) Has neither credit card (3). Has exactly one of the two credit cards.

Explanation / Answer

a.)

1.) P( thestudent has a master card) = (2500/10000) = 0.25

2.) P( has a VISA) = (4000/10000) = 0.4

3.) P( has both credit cards) = (1000/10000) = 0.1

b.) P( has a MasterCard or a VISA)

= P( has a MasterCard) + P( has a VISA) - P(both MasterCard and VISA)

= (2500/10000) + (4000/10000) - (1000/10000)

= (5500/10000)

= 0.55

2.) P( has neither cards) = 4500/10000 = 0.45

3.) P( exactly one of the two credit cards)

= (1500 + 3000)/10000

= 0.45

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