An instructor feels that 15% of students get below a C on their final exam. She decides to look at final exams (selected randomly and replaced in the pile after reading) until she finds one that shows a grade below a C. We want to know the probability that the instructor will have to examine at least ten exams until she finds one with a grade below a C. What is the probability question stated mathematically?

We are given,

An instructor feels that $15\%$of students get below a C on their final exam.

She finds one that shows a grade below a C after looking at final exam.

In statistics, the geometric distribution is one of the discrete probability distribution. In a Bernoulli trial, the probability of the number of successive failures before a success is obtained is represented by a geometric distribution, which is a sort of discrete probability distribution. A random variable is said to have geometric distribution if the probability mass function is:

$P(X=x)p{q}^{x-1},x=1,2,3,4$

We clearly see, that X denotes instructor will have to examine at least ten exams until she finds one with a grade below a C.

The given statement states that probability the instructor will have to examine at least ten exams until she finds one with a grade below a C. Mathematically it can be expressed as:

$P(x\ge 10).$