Hey!!

At a gaming machine the probability of winning is 25%. A player plays 20 rounds.

- Which is the probability that he wins exactly five times?
- Which is the probability that in ten rounds he wins five times?
- Which is the probability that in ten rounds he wins ten times?
- Which is the probability that in twenty tries he wins zero times?

Do we use at each case the binomial distribution?

- $$P(5\mid 20)=\binom{20}{5}0.25^5\cdot 0.75^{15}$$
- $$P(5\mid 10)=\binom{10}{5}0.25^5\cdot 0.75^{5}$$
- $$P(10\mid 10)=\binom{10}{10}0.25^{10}\cdot 0.75^{0}$$
- $$P(0\mid 20)=\binom{20}{0}0.25^0\cdot 0.75^{20}$$