SOLUTION: Suppose that P(A) = 0.3 and P(A ∩ B) = 0.06. Find P(B|A).

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Question 1206244: Suppose that
P(A) = 0.3
and
P(A ∩ B) = 0.06.
Find
P(B|A).
Found 3 solutions by Theo, ikleyn, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
p(A) = .3
p (A and B) = .06
p(B given A) = p(A and B) / p(A) = .06 / .3 = .2
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Suppose that P(A) = 0.3 and P(A ∩ B) = 0.06.
Find P(B|A).
~~~~~~~~~~~~~~~~~~ 

P(B|A) is the conditional probability that event B will happen given that event A happens.

                              P(A ∩ B)
By the definition,  P(B|A) = ----------.
                                P(A)


Substitute the numbers and get  P(B|A) =  =  = 0.2.    ANSWER

Solved.



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

The basic definition of probability is this:

               # of ways event can happen
  P(event) = ------------------------------
              total # of possible outcomes

By definition, P(B|A) is the probability that B happens, given that A happens.

With that definition, the denominator of the probability fraction is the probability that A happens, because the only part of the sample space you are concerned with is the outcomes in which A happens.  And the numerator is the probability that both A and B happen:

            P(A ∩ B)
  P(B|A) = ----------
              P(A)

In your problem, the given information is the numerator and denominator of this fraction, so

            .06
  P(B|A) = ----- = 0.2
            0.3
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