Question:
Aand B are equally good tennis players .which of the following two events is more probable 1. A beats B in exactly 3 games out of 4 2. 1. A beats B in exactly 5 games out of 8
Answer:
Given A and B are equally good tennis players.
So, P(A) = P(B) = 1/2
Now, Probability of A beating B in exactly 3 games out of 4 = 4C3 * (1/2)3 *(1/2)
= 4C1 * (1/2)4
= 4/16
= 1/4
= 0.25
Again, Probability of A beating B in exactly 5 games out of 8 = 8C5 * (1/2)5 *(1/2)3
= 8C3 * (1/2)8
= (8*7*6)/(3*2*1) * (1/256)
= (8*7*6)/(6*1) * (1/256)
= (8*7)/256
= 7/32
= 0.219
So, the first event is more probable.
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