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## Homework Statement

Ten cards are face down in a row on a table. Exactly one of them is an ace. You turn the cards over oen at a time, moving from left to right. Let X be the random variable for the number of cards turned before the ace is turned over. What is the probability function for X?## Homework Equations

P(a|b)=P(a&b) / P(B)

## The Attempt at a Solution

P(X=0) = P(1st card is the ace)=1/10P(X=1)=P(2nd card is the ace|1st card is not ace) * P(1st card is not ace)=9/10 * 1/9

P(X=2)=9/10 * 8/9 * 1/8 = 1/10

so p(x)=1/10 for x=0,1,...,9

I am having trouble understanding how the book arrived at the solution. For P(X=1), it appears to me that they manipulated the equation P(a|b)=P(a&b) / P(B) to be P(a|b) * P(b) = P(a&b). So they are solving for P(a&b). But isn't the key to solve for P(a|b)?