A high school probability problem.

(1) is an independent repeated experiment,

One shot five times, the probability of hitting the target exactly three times is p.

Then p = c (5 5,3) * (2/3) 3 * (1-2/3) 2 =10 * (8/27) * (19) = 80/243.

(2) One shot was stopped just after it was hit five times.

Then the fourth time and the fifth time missed the target, and the third time must hit the target.

Hit the target at least once for the first time and the second time.

There are the following three categories

① the miss probability p1= (2/3) * (1/3) * (2/3) * (1/3) * (1/3) = 4/243.

② Failure probability P2 = (2/3) * (2/3) * (2/3) * (1/3) * (1/3) = 8/243.

③ Miss probability P3 = (1/3) * (2/3) * (2/3) * (1/3) * (1/3) = 4/243.

∴a Probability of stopping shooting after five shots, p'

Then p' = p1+p2+P3 =16/243.