Find find P(B\A)?

Question

The probability that event A occurs is .41. The probability that event B occurs is .62. The probability that both events A and B occur is .25,
find P(B\A).
Round your answer to two decimal places.

Answer 1

P(B\A) = P(B) - P(B∪A) = .62 - .25 = .37

Edit: Were you looking for probability of B given A or probability of B∧¬A? If the former, you should use the pipe symbol " | " rather than a backslash, which is usually used to indicate set subtraction. On American keyboards, the pipe symbol is input by shift-backslash (it will look like a broken line on your keyboard, but nearly all modern computers render it as a single vertical line).

Answer 2

I think you are looking for P(B|A). This is the probability of event B happening given A has happened.

This is kinda a trick problem in the sense that A and B are nearly independent.
0.62 * 0.41 = 0.2542
This is nearly equal to 0.25, and equal to two decimal points.

What this means is that B is fairly independent of A therefore:
P(B|A) = .62

---- EDIT ----

Hmm... Hayhabr may be right...

EDIT

Hehe, he edited his answer. I was wondering how it was so different from mine. His is correct, but you should understand how it is that I was able to avoid using Bayes rule (which is what he used).

Answer 3

P(B given A) = P(B and A) / p(A)

= .25/..41

=.60975...

= .61

Edited