Question

The following is a table of probabilties calculated from a survey of BHCC students with the question asked "How many classes are you taking this semester?" X: # of classes 1 2 3 4 5 P(x) 0.16 0.3 0.11 0.35 0.08 Using the table, find the following probabilities for a student selected at random: What is the probability that a student is taking no more than 2 clases?

Answer 1

Let X be the number of classes a student is taking. We are asked for the probability that a student is taking no more than 2 clases, this translates the fact that X<=2. That is, X is either 1 or 2. Since the events of taking 1 or taking 2 classes are exclusive (meaning that it cannot happen that a student takes 1 class and takes 2 classes at the same time), then

$P(X\le2)\text{ = P(X=1)+P(X=2)}$

In our table, P(X=1) = 0.16 and P(X=2) = 0.3. Then

$P(X\le2)\text{ = P(X=1)+P(X=2)=0.16+0.3 = 0.46}$