Of the 10,000 college students, 2500 have a master card (M), 4000 have visa (V)

ID: 3066735 • Letter: O

Question

Of the 10,000 college students, 2500 have a master card (M), 4000 have visa (V) and 1000 have both.

Find the probability that a randomly selected student has

a. Mastercard

b. Visacard

c. both cards

Fill in the contingency table summarizing the credit cards data. Employ the following pairs of events: M and not M, V and not V

Events

Have Visa card (V)

Does not have visa card (V)

Total

Master card (M)

Does not have a masters card (M)

Total

Use the contingency table to find the probability that a randomly selected student has

a. Master card or a visa

b. Neither credit card

c. Exactly one of the two cards

Events

Have Visa card (V)

Does not have visa card (V)

Total

Master card (M)

Does not have a masters card (M)

Total

Ans:

a)P(master card)=2500/10000=0.25

b)P(visacard)=4000/10000=0.40

c)P(both cards)=1000/10000=0.1

Uisng contigency table:

a)P(master or visa)=P(master)+P(visa)-P(master and visa)=0.25+0.4-0.1=0.55

b)P(neiher)=1-0.55=0.45

c)P(exactly one of the two)=(3000+1500)/10000=0.45

Events Visa card not visa Total Master(M) 1000 1500 2500 Not master 3000 4500 7500 Total 4000 6000 10000

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