Answer:
There is a 25.52% probability of observating 4 our fewer succesful recommendations.
Step-by-step explanation:
For each recommendation, there are only two possible outcomes. Either it was a success, or it was a failure. So we use the binomial probability distribution to solve this problem.
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.
In this problem we have that:
If the claim is correct and the performance of recommendations is independent, what is the probability that you would have observed 4 or fewer successful:
This is
In which
There is a 25.52% probability of observating 4 our fewer succesful recommendations.