Question

presented is a probability distribution for the number of motor vehicles: cars, trucks, or motorcycles owned by a random family. because almost no families own more than five, we will combine any families with more than five into that value.

vehicles	probability
1	0.15
2	0.35
3	0.28
4	0.09
5	0.05

what is the probability a randomly selected family has at least one vehicle?

answer to two decimal places:

Explanation:

Step1: Recall the complement rule

The probability of an event \( A \) is \( P(A) = 1 - P(\text{not } A) \). Here, the event "at least one vehicle" is the complement of "0 vehicles".

Step2: Find \( P(0 \text{ vehicles}) \)

From the table, \( P(0 \text{ vehicles}) = 0.08 \).

Step3: Calculate \( P(\text{at least 1 vehicle}) \)

Using the complement rule: \( P(\text{at least 1 vehicle}) = 1 - P(0 \text{ vehicles}) = 1 - 0.08 = 0.92 \).

Answer:

0.92