Question

4.11... Of 10,000 students at a college, 2,500 have a Mastercard (M), 4,000 have a VISA (V), and 1,000 have both.

a. Find the probability that a randomly selected student

(1) Has a Mastercard.
(2) Has a VISA.
(3) Has both credit cards.

b. Construct and fill in a contingency table summarizing the credit card data. Employ the following pairs of events: M and _M , V and _ . ￣ V￣

c. Use the contingency table to 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.

Answer 1

Answer on Question #44238 – Math – Statistics and Probability

Question:

Of 10,000 students at a college, 2,500 have a Mastercard (M), 4,000 have a VISA (V), and 1,000 have both.

a. Find the probability that a randomly selected student

(1) Has a Mastercard.

(2) Has a VISA.

(3) Has both credit cards.

b. Construct and fill in a contingency table summarizing the credit card data. Employ the following pairs of events: M and _M, V and _.

c. Use the contingency table to 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.

Solution.

a. (1) The probability that a randomly selected student has a Mastercard is: $\frac{2500}{10000} = \frac{1}{4} = 0.25$

Answer. 0.25

(2) The probability that a randomly selected student has a VISA is: $\frac{4000}{10000} = \frac{2}{5} = 0.4$

Answer. 0.4

(3) The probability that a randomly selected student has both credit cards is: $\frac{1000}{10000} = \frac{1}{10} = 0.1$

Answer. 0.1

b. A contingency table summarizing the credit card data:

c. Use the contingency table to find

(1) The probability that a randomly selected student has a Mastercard or a VISA is:

$$\frac{1000 + 1500 + 3000}{10000} = \frac{5500}{10000} = 0.55$$

Answer. 0.55

(2) The probability that a randomly selected student has neither credit card is: $\frac{4500}{10000} = 0.45$

Answer. 0.45

(3) The probability that a randomly selected student has exactly one of the two credit cards is:

$$\frac{3000 + 1500}{10000} = 0.45$$

Answer. 0.45

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