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? 0.080 (completed) the probability of having less than 3 accidents in a year is
accidents: x | 0 | 1 | 2 | 3
probability: p(x) | 0.905 | 0.080 | 0.010 | 0.005

Explanation:

First Sub - Question: Probability of exactly 1 accident

Step1: Identify the relevant probability

We are looking for the probability of having exactly 1 accident in a year. From the probability distribution table, when \(X = 1\) (where \(X\) represents the number of accidents), the probability \(P(X = 1)\) is given directly in the table.

Step2: Read the value from the table

Looking at the row where \(X = 1\) and the column for \(P(X)\), we can see that \(P(X = 1)=0.080\).

Second Sub - Question: Probability of less than 3 accidents

Step1: Understand the event "less than 3 accidents"

The event of having less than 3 accidents means having 0, 1, or 2 accidents. So we need to find \(P(X<3)=P(X = 0)+P(X = 1)+P(X = 2)\).

Step2: Get the probabilities from the table

From the table, \(P(X = 0)=0.905\), \(P(X = 1)=0.080\), and \(P(X = 2)=0.010\).

Step3: Calculate the sum

\(P(X<3)=0.905 + 0.080+0.010\)
\(=0.905+0.090\)
\(= 0.995\)

Answer:

0.080