# Thread: Gaming machine : The probability of winning

1. Hey!!

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

1. Which is the probability that he wins exactly five times?
2. Which is the probability that in ten rounds he wins five times?
3. Which is the probability that in ten rounds he wins ten times?
4. Which is the probability that in twenty tries he wins zero times?

Do we use at each case the binomial distribution?

1. $$P(5\mid 20)=\binom{20}{5}0.25^5\cdot 0.75^{15}$$
2. $$P(5\mid 10)=\binom{10}{5}0.25^5\cdot 0.75^{5}$$
3. $$P(10\mid 10)=\binom{10}{10}0.25^{10}\cdot 0.75^{0}$$
4. $$P(0\mid 20)=\binom{20}{0}0.25^0\cdot 0.75^{20}$$

2. We are making the assumption that the gaming machine is fair that is that the the goes are independent. If this is the case then your results are indeed correct. Well done