Answer:
0.0039 = 0.39% probability that she beats all 4 levels on the first try.
Step-by-step 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.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
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
Janice plays through 4 levels.
This means that
What is the probability that she beats all 4 levels on the first try?
This is P(X = 4). So
0.0039 = 0.39% probability that she beats all 4 levels on the first try.