Probability?? Someone please help!

Question

anonymous · Answer

The probability that a student takes a history class and a sociology class is 0.051. The probability that a student takes a history class is 0.32. What is the probability that a student takes a sociology class given that the student is taking a history class?

anonymous · Answer

0.051

 0.159

 0.269

 0.32

anonymous · Answer

I'm more confused on the question than the answer.

kirbykirby · Answer

This is a conditional probability. $$P(A |B)=\frac{P(AB)}{P(B)} $$

anonymous · Answer

I'm more confused on the question. The question at the end is just asking for the first sentence, is it not? Or am I missing something or reading it wrong. The way I'm reading it, it would be 0.051 or 0.32

kirbykirby · Answer

No. you are given these quantities: 
Denote H = taking history
S = taking sociology

$P(H\cap S)=0.051 $
$P(H)=0.32)$
And they are asking for $P(S|H)$

anonymous · Answer

Wait. I think I might know. Tell me if I'm correct please? To make it short: $$\frac{ 0.051 }{ 0.32 }=0.159$$

anonymous · Answer

That's what makes sense to me but I'm not sure 100%

kirbykirby · Answer

Yep indeed.

anonymous · Answer

Okay, thanks for helping!

kirbykirby · Answer

np