Mathematical probability problem in senior high school

(1) hit 1 times, p = c (1, 3) * (4/5) * (1/5) * (1/5) = 3 * (4//kloc).

= 12/ 125

Hit three times, p = c (3 3,3) * (4/5) * (4/5) * (4/5) = 64/125.

p = 12/ 125+64/ 125 = 76/ 125

(2) It is easy to calculate that the probability of hitting 0 times with three shots is1125.

The probability of hitting twice is1-1125-76/125 = 48/125.

So the probability of hitting 0 times with 4 guns is 4/5 *1125 = 4/625.

The probability of four shots hitting 1 time is1125 *1/5+12/125 * 4/5 = 49/625.

The probability of four shots hitting twice is 48/125 * 4/5+12/125 *1/5 = 204/625.

The probability of hitting three times with four shots is 48/125 *1/5+64/125 * 4/5 = 304/625.

The probability of four shots hitting four times is1/5 * 64/125 = 64/625.

It is distributed. good play

e \ = 49/625+2 * 204/625+3 * 304/625+4 * 64/625 = 13/5