Question

Identify the parameters p and n in the following binomial distribution scenario. The probability of winning an arcade game is 0.718 and the probability of losing is 0.282. If you play the arcade game 20 times, we want to know the probability of winning more than 15 times. (Consider winning as a success in the binomial distribution.)

Answer 1

p = 0.718 and n = 20

Explanation:

p is the probability of success and n is the number of trials.

Here, p = 0.718 and n = 20.

Answer 2

There is a 29.50% probability of winning more than 15 times.

Explanation:

For each time you play the arcade game, there are only two possible outcomes. Either you win, or you lose. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinatios of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

In this problem we have that:

The probability of winning a game is 0.718. So
`p = 0.718`.

The game is going to be played 20 times, so
`n = 20`.

If you play the arcade game 20 times, we want to know the probability of winning more than 15 times.

This is

`P(X > 15) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.2950`.

There is a 29.50% probability of winning more than 15 times.