The probability that a randomly selected student at UW is a woman is 0.52. The p
ID: 3221132 • Letter: T
Question
The probability that a randomly selected student at UW is a woman is 0.52. The probability that a randomly selected student is studying education is 0.15. The conditional probability that the student is a man, given that the student is studying education is 0.4. a) What is the conditional probability that the student is a woman given that the student is studying education? b) What is the probability that a randomly selected student is male and studies education? c) What is the probability that a randomly selected student is female and studies education? d) What is the probability that a randomly selected student is a man? e) What is the conditional probability that the student is studying education give the student is a man?Explanation / Answer
W : Event of a randomly selected student is Women ; P(W) = 0.52
M : Event of a randomly selected student is a man ; P(M) = 1- 0.52 = 0.48
E : Event of a randomly selected student is studying education : P(E) = 0.15
Conditional probability that student is a man given that the student is studying education = P(M|E) = 0.4
(a) Conditional Probability that the student is woman given that the student is studying eudcation = P(W|E)
P(W|E) = 1- P(M|E) = 1-0.4=0.6
Conditional Probability that the student is woman given that the student is studying eudcation = P(W|E) = 0.6
(b) Probablity that a randomly selected student is male and studies Education =P(M and E)
By multiplication theorem,
P(M and E) = P(E) P(M|E) = 0.15 x 0.4 = 0.06
Probablity that a randomly selected student is male and studies Education =P(M and E) = 0.06
(c) Probability that randomly selected student is female and studies Education = P(F and E)
By multiplication theorem,
P(F and E) = P(E) P(F|E) = 0.15 x 0.6 = 0.09
Probability that randomly selected student is female and studies Education = P(F and E) = 0.09
(d) Probability that rndomly selected student is man = P(M)
P(M) = 1- P(W) = 1-0.52 = 0.48
Probability that rndomly selected student is man = 0.48
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