Question

A slot machine at a hotel is configured so that there is a 1/1400 probability of winning the jackpot on any individual trial. If a guest plays the slot machine 8 times, find the probability of exactly 2 jackpots. If a guest told the hotel manager that she had hit two jackpots in 8 plays of the slot machine, would the manager be surprised?

Answer 1

It is said that the guest wins 2 times out of the 8 trials. So the number of ways to win 2 times out of 8 is 8P2 = 56.

The probability of winning is 1/1400. Therefore, the probability of losing is 1-1/1400 = 1399/1400.

Therefore, the probability of winning 2 times out of the 8 trials, and the rest 6 trials being a loss is:

$56*(\frac{1}{1399} )^2*(\frac{1}{1400})^6=3.8*10^{-24}$. Which is an extremely low probability. Therefore, the manager would be surprised for sure.

Answer 2

Answer: 0.0000142; yes, 2 J's in 8 plays is extremely small!