Question 1194098
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The response from tutor @ikleyn shows the conditional probability formula and a full solution to the problem.<br>
The response also states that the concept of conditional probability is difficult for beginners.<br>
That was true for me; and I see it often among students first working with the concept.<br>
So let me take a moment to try to explain why the formula is what it is.<br>
The basic probability equation is<br><pre>
                            good outcomes
  P(desired outcome) = ------------------------
                        all possible outcomes</pre>
The conditional probability P(U|V) is the probability that U happens, GIVEN THAT V happens.  That means the only outcomes we are considering are those in which V happens -- so the denominator of the probability fraction ("all possible outcomes") is P(V).<br>
Then the numerator of the probability fraction ("good outcomes") is the probability that U ALSO happens (i.e., U and V BOTH have to happen) -- so the numerator is P(U AND V).<br>
And so the conditional probability formula is<br><pre>
            P(U AND V)
  P(U|V) = ---------------
               P(V)</pre>