Question

Janice has just bought a new pack of levels in her favorite game, Candy Crush. She knows that she can win a new level on the first try 25% of the time, and that whether or not she beats one level on the first try will not have any effect on whether or not she beats a different level on the first try. Janice plays through 4 levels. What is the probability that she beats all 4 levels on the first try

Answer 1

0.0039 = 0.39% probability that she beats all 4 levels on the first try.

Explanation:

For each level, there are only two possible outcomes. Either she can win the new level on the first try, or she cannot. The probability of winning a level on the first try is independent of any other level. This means that the binomial probability distribution is used to solve this question.

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 combinations 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.

She knows that she can win a new level on the first try 25% of the time.

This means that
`p = 0.25`

Janice plays through 4 levels.

This means that
`n = 4`

What is the probability that she beats all 4 levels on the first try?

This is P(X = 4). So

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

`P(X = 4) = C_(4,4).(0.25)^(4).(0.75)^(0) = 0.0039`

0.0039 = 0.39% probability that she beats all 4 levels on the first try.