Questions: The probability a car salesman sells a car to a customer is 0.05 Assuming the salesmen sees 10 customers in a week, what is the probability he sells less than 2 cars? Write answer using three decimal places

The probability a car salesman sells a car to a customer is 0.05 Assuming the salesmen sees 10 customers in a week, what is the probability he sells less than 2 cars? Write answer using three decimal places

Transcript text: The probability a car salesman sells a car to a customer is 0.05 Assuming the salesmen sees 10 customers in a week, what is the probability he sells less than 2 cars? Write answer using three decimal places

Solution

Solution Steps

Step 1: Define the Problem

We are tasked with finding the probability that a car salesman sells less than 2 cars in a week, given that the probability of selling a car to a customer is \( p = 0.05 \) and he sees \( n = 10 \) customers.

Step 2: Calculate the Probability of Selling 0 Cars

Using the binomial probability formula:

\[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{n-x} \]

where \( q = 1 - p = 0.95 \). For \( x = 0 \):

\[ P(X = 0) = \binom{10}{0} \cdot (0.05)^0 \cdot (0.95)^{10} = 0.599 \]

Thus, the probability of selling 0 cars is:

\[ P(X = 0) = 0.599 \]

Step 3: Calculate the Probability of Selling 1 Car

Using the same formula for \( x = 1 \):

\[ P(X = 1) = \binom{10}{1} \cdot (0.05)^1 \cdot (0.95)^{9} = 0.315 \]

Thus, the probability of selling 1 car is:

\[ P(X = 1) = 0.315 \]