In a survey of 100 college students in Kalamazoo County 55 h

In a survey of 100 college students in Kalamazoo County, 55 had taken courses at KVCC, 75 had taken courses at WMU, and 47 had taken courses at both. (show work)

A. How many had taken courses at either KVCC or WMU?

B. How many had taken courses at neither KVCC nor WMU?

C. What is the probability that a student had taken courses only at KVCC?

D. Given that a student had taken courses at KVCC, what is the probability she also took courses at WMU?

Solution

Note that

N = N(K) + N(W) - N(W and K) + N(none)

Thus,

100 = 55 + 75 - 47 + N(none)

N(none) = 17

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A.

N(K or W) = N(K) + N(W) - N(K and W)

= 83

Thus,

P(K or W) = 83/100 = 0.83 [ANSWER]

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B.

p(none) = 17/100 = 0.17 [ANSWER]

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C.

P(K) = 55/100 = 0.55

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D.

P(W|K) = N(W and K)/N(K) = 47/55 = 0.854545455 [ANSWER]