Question

Do you carpool? Let X represent the number of occupants in a randomly chosen car on a certain stretch of highway during morning commute hours. A survey of cars showed that the probability distribution of X is as follows.c. Find the probability that a car has only one occupant.d. Find the probability that a car has fewer than four occupants.

Answer 1

To solve this exercise we must take into account the given table

c. Find the probability that a car has only one occupant.

Since x is the number of people in the car, the probability that the car has only one passenger is:

$P_1=0.7$

d. Find the probability that a car has fewer than four occupants.

If we want to make the probability that a car has less than 4 people, we have to add the probabilities from 1 to 3

$\begin{gathered} P_{<4}=P_1+P_2+P_3 \\ P_{<4}=0.7+0.15+0.10 \\ P_{<4}=0.95 \end{gathered}$