Question

in a survey, 100 people were asked how many car accidents they had in the past year. the estimated probability distribution for the number of accidents is shown in the table. using the data from the table, what is the probability of having exactly 1 accident in a year? the probability of having less than 3 accidents in a year is

Explanation:

Step1: Understand the problem

We need to find the probability of having less than 3 accidents. Less than 3 means \(X = 0\), \(X=1\), or \(X = 2\).

Step2: Use the formula for the sum of probabilities

The formula for the probability of a compound event (sum of mutually - exclusive events) is \(P(X<3)=P(X = 0)+P(X = 1)+P(X = 2)\).
Substitute the values from the table: \(P(X = 0)=0.905\), \(P(X = 1)=0.080\), \(P(X = 2)=0.010\).

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Answer:

\(0.995\)