Question

The probability that a participant is happy is p(h) = .55. the probability that a participant is employed is p(e) = .65. the probability that a participant is employed given that she is happy is p(e/h) = .73. using the formula for bayes' theorem, what is the probability that a participant is happy, given that the participant is employed?

Answer 1

Given:
p(e/h) = 0.73
p(h) = 0.55
p(e) = 0.65

What we want to find
p(h/e)
which represents the probability of finding a happy person given they are employed

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We'll use Bayes' Theorem which says
p(a/b) = p(b/a)*p(a)/p(b)

So this means
p(h/e) = p(e/h)*p(h)/p(e)
p(h/e) = 0.73*0.55/0.65
p(h/e) = 0.61769 (this is approximate)
p(h/e) = 0.62 (rounding to 2 decimal places)

The answer to two decimal places is approximately 0.62