Astudent is taking an exam consisting of three questions selected randomly from a list of 100 questions. to pass, he needs to answer all three questions. what is the probability that the student will pass the examination if he knows the answers to 90 questions on the list?

The probability that the student will pass is 72.6%

Step-by-step explanation:

There are 100 questions total.

The order that the questions are selected makes no diffence. For example, if  Q3, Q28, Q57 are selected in this order or as Q28, Q57, Q3, it is the same exam. So it is a combination problem.

Combination Formula:

A combination of n elements from a set of m objects has the following formula:

Probability:

The probability is the number of desired outcomes divided by number of total outcomes.

The number of total outcomes is the combination of 3 questions from a set of 100 questions. So, we have n = 3, m = 100.

There are 161700 total outcomes.

The number of desired outcomes is the combination of 3 questions from a set of 90 questions(the questions that the student knows the answers). So, we have n = 3, m = 90.

Probability P = D/T = 117480/161700 = 0.726 = 72.6%

The probability that the student will pass is 72.6%