A fair coin is tossed 10 times. The total number of heads in the first 5 tosses is
denoted by X. If the total number of tails is 6 (event A), what is the conditional
PMF pX|A(x) of X?
$\displaystyle X= $ # heads in first $\displaystyle 5$ tosses.
$\displaystyle A= \{$# $\displaystyle tails = 6\}$
$\displaystyle p_X|A (x) = \frac{p(X=i,A)}{P(A)} = \frac{{4\choose i}(1-\frac{1}{2})^{4-i-10}(\frac{1}{2})^{4-i}}{{10\choose 6}(1-\frac{1}{2})^4(\frac{1}{2})^6}$
This needs some work....
Anyone have ideas...?