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Question

An archer has a 25% chance of hitting the bullseye on a target. What is the probability that the archer will hit the bullseye at most three out of five times? Round your percent answer to the nearest hundredth

Answer 1

Probability of at most 3 hits out of 5 is the same as

1 minus the probability of 4 or 5 hits, P(4 or 5) =1/64.

Prob(0 or 1 or 2 or 3) = 63/64 = 0.98 about 98%

P(5 hits) = (1/4)^5

P(4 hits) = 5((1/4)^4(3/4) = 15(1/4)^5

P(4 or 5) = 16/4^5 = 4^2/4^5 = 1/4^3 = 1/64

P(0 to 3) = 1-1/64 = 63/64 = 0.98 rounded off to nearest hundredth

There's only one way to get 5 out 5 hits. Each is with probability 1/4. so multiply 1/4 by 1/4 by 1/4 by 1/4 by 1/4. There's 5 ways to get 4 out of 5 hits: HHHHM, HHHMH, HHMHH, HMHHH, or MHHHH

each of the 5 ways has probability (1/4)^4(3/4)