Question

A slot machine at a hotel is configured so that there is a 1/1200 probability of winning the jackpot on any individual trial. If a guest plays the slot machine 6 times, find the probability of exactly 2 jackpots. If a guest told the hotel manager that she had hit two jackpots in 6 plays of the slot machine, would the manager be surprised?

Answer 1

Answer:

The probability is approximately one in a million (0.001% ).

It's a very little probability, so the manager would be really surprised.

Step-by-step explanation:

We have for this question to calculate with a binomial random variable, with n=6 and p=1/1200=0.00083 .

We have to calculate the probability of getting 2 hits in the sample of size 6.

$P(x=2)=\binom{6}{2}p^2(1-p)^4=15*(1/1200)^2*(1199/1200)^4\\\\P(x=2)=15* 0.000000694*0.996670831= 0.00001038$

The probability is approximately one in a million (0.001% ).

It's a very little probability, so the manager would be really surprised.