Suppose that at the shooting range you take 10 shots at the target, with a .75 p

Question

Suppose that at the shooting range you take 10 shots at the target, with a .75 probability on each shot of hitting the target. Assume that each shot is independent of all the others. To find the probability of exactly 6 hits and 4 misses (in any order), the formula requires us to compute

C(10,6)(.75)6(.25)4

a) If we just computed (.75)6(.25)4 without multiplying by C(10,6), of what event would that be the probability?

b. Why must we multiply (.75)6(.25)4 by C(10,6) when we answer the original question about 6 hits and 4 misses? What, specifically, does the factor of C(10,6) account for?

Explanation / Answer

It takes a particular pattern of 6 hits and 4 misses. Like first 6 being hits out of 10 shots or last six being 6 hits.

We are trying to arrange 6 hits and 4 misses . This can be done in C(10,6). . That is 6 hits can occupy 10 places in C(10,6) ways. We consider all of them in (b) while we consider only one particular one in first case (a)

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