Question

professors sometimes select a student at random to answer a question. if there are 15 people in class and professor maxwell asks 3 questions, what is the probability that you will not be selected? assume that he will not pick the same person twice in a given lecture. write answer as a fraction.

Explanation:

Step1: Calculate probability of not being selected for first question

There are 14 non - you people out of 15 for the first question. So the probability is $\frac{14}{15}$.

Step2: Calculate probability of not being selected for second question

After the first non - you selection, there are 13 non - you people out of 14 for the second question. So the probability is $\frac{13}{14}$.

Step3: Calculate probability of not being selected for third question

After the first two non - you selections, there are 12 non - you people out of 13 for the third question. So the probability is $\frac{12}{13}$.

Step4: Calculate overall probability

Since these are independent events, we multiply the probabilities: $\frac{14}{15}\times\frac{13}{14}\times\frac{12}{13}=\frac{12}{15}=\frac{4}{5}$.

Answer:

$\frac{4}{5}$