The probability table given here represents the results of a census conducted of

Question

The probability table given here represents the results of a census conducted of all students in a large university. Each student was categorized by gender (M/F) and by whether or not they answered affirmatively to a question as to whether they had been inebriated in the past 30 days (I/I bar). Use the probability notation of this chapter to characterize each of the following. Then use the table entries to find the indicated probability. a) The probability that a student, randomly selected from among the female's, will not have been inebriated in the past 30 days. b) The probability that a randomly selected student will be female. c) The probability that a randomly selected student will be male or will have been inebriated in the past 30 days.

Explanation / Answer

Probability of female, P(F) = 0.46
Probability of male, P(M) = 0.54

(a)
Probability that a student randomly selected from amonth the females will not have inherited in the part 30 days
P(I'|F) = P(F|I')*P(I')/(P(F|I)*P(I) + P(F|I')*P(I'))
P(I'|F) = 0.36*0.68/(0.1*0.32 + 0.36*0.68) = 0.8844

(b)
Probability that randomly selected student is female = 0.46

(c)
P(M) = 0.54
P(I') = 0.68
P(M and I') = 0.36

P(M or I') = P(M) + P(I) - P(M and I')
P(M or I') = 0.54 + 0.68 - 0.36 = 0.86

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