SOLUTION: Wally and Sally each toss a fair coin 8 times. Determine the probability that Sally tossed exactly 5 more heads than did Wally. Express your answer as a common fraction reduced to

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Question 1055381: Wally and Sally each toss a fair coin 8 times. Determine the probability that Sally tossed exactly 5 more heads than did Wally. Express your answer as a common fraction reduced to lowest terms.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So the probability for both Wally and Sally for number of heads would be calculated,

So then find the joint probability when Sally has 5 more than heads than Wally
Sally-5, Wally-0: P=%281%2F256%29%2856%2F256%29=56%2F256%5E2
Sally-6, Wally-1: P=%288%2F256%29%2828%2F256%29=224%2F256%5E2
Sally-7, Wally-2: P=%2828%2F256%29%288%2F256%29=224%2F256%5E2
Sally-8, Wally-3: P=%2856%2F256%29%281%2F256%29=56%2F256%5E2
So summing those together,
P=%2856%2B224%2B224%2B56%29%2F256%5E2=560%2F256%5E2=35%2F4096