a student goes to class on a snowy day with probability of 0.4, but on a nonsnow

Question

a student goes to class on a snowy day with probability of 0.4, but on a nonsnowy day attends with a probability 0.7. suppose that 20% of the days in February are snowy. what is the probability that it snowed on February 7 given that the student was in class on that day? a student goes to class on a snowy day with probability of 0.4, but on a nonsnowy day attends with a probability 0.7. suppose that 20% of the days in February are snowy. what is the probability that it snowed on February 7 given that the student was in class on that day? a student goes to class on a snowy day with probability of 0.4, but on a nonsnowy day attends with a probability 0.7. suppose that 20% of the days in February are snowy. what is the probability that it snowed on February 7 given that the student was in class on that day?

Explanation / Answer

Let

A = attended
S = snowy

Hence, by Bayes' Rule,

P(A) = P(S)P(A|S) + P(S')P(A|S') = 0.20*0.4 + (1-0.20)*0.7 = 0.64

Hence,

P(S|A) = P(S) P(A|s)/P(A) = 0.20*0.4/0.64 = 0.125 [ANSWER]

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