The probability that a student passes a class is p(P) = 0.56. The probability that a student...

Question:

The probability that a student passes a class is p(P) = 0.56. The probability that a student studied for a class is p(S) = 0.54. The probability that a student passes a class given that he or she studied for the class is p(P / S) = 0.71.

What is the probability that a student studied for the class, given that he or she passed the class (p(S / P))?

Given that,

{eq}P(p) = 0.56\\ P(s) = 0.54\\ P(p|s) = 0.71 {/eq}

Now,

Usding conditiona probability:

{eq}P(p|s) = \frac{P(p \cap s)}{P(s)}\\ 0.71 = \frac{P(p \cap s)}{0.54}\\ P(p\cap s) = 0.54\times 0.71\\ P(p\cap s) = 0.383 {/eq}

The required probability is {eq}P(s|p). {/eq}

So,

{eq}P(s|p) = \frac{P(s \cap p)}{P(p)}\\ P(s|p) = \frac{0.383}{0.56}\\ \fbox{P(s|p) = 0.684} {/eq}