Probability (my ans is wrong.. x.x)?

Question

If P(A|B) = 2/5, P(B) = 1/4, P(A) = 1/3, find

(a) P(B|A);

My workings:

P(B|A) = P(B and A) / P(A) = (7/12) / 1/3 = 7/4...

The answer is 0.3...

Help...

Answer 1

P(AlB) = P(A∩B) / P(B)

=> 2/5 = P(A∩B) / (1/4)

=> P(A∩B) = (2/5)(1/4) = 1/(10)

P(BlA)

= P(A∩B) / P(A)

= (1/10) / (1/3)

= 0.30.

Answer 2

Use Bayes rule here. This is another one of those really important equations that will be useful many times later on.

As you say, it's correct that

P(B|A) = P(A and B) / P(A)

However, you don't directly know P(A and B). So, another way to write it is this:

P(B|A) = P(A|B) * P(B) / P(A)

so, plugging in,

P(B|A) = 2/5 * 1/4 / (1/3) = 3/10 = 0.3