What is the probability that a randomly selected student will fail an exam if 100 out of 120 are expected to pass?

• A. 1/5
• B. 1/6
• C. 1/4
• D. 1/3

Answer: (B)

To determine the probability that a randomly selected student will fail the exam, we first need to analyze the information given. Out of 120 students, 100 are expected to pass. This implies that the number of students who are expected to fail is:

120 total students - 100 students passing = 20 students failing.

Now, to find the probability of a student failing the exam, we can use the formula for probability, which is the number of favorable outcomes divided by the total number of outcomes. In this case, the number of favorable outcomes is the number of students who fail the exam (20), and the total number of outcomes is the total number of students (120).

So, the probability of failing is calculated as follows:

Probability of failing = Number of students failing / Total number of students

= 20 / 120

= 1 / 6.

This result indicates that the probability of selecting a student who will fail the exam is 1/6, which aligns with the correct answer. Understanding the relationship between the total number of students, those passing, and those failing is crucial in calculating probabilities accurately.