The probability a car salesman sells a car to a customer is 0.05
Assuming the salesmen sees 13 customers in a week, what is the probability he sells less than 2 cars?
Answer
Final Answer: The probability that the car salesman sells less than 2 cars in a week is approximately \(\boxed{0.865}\).
Step 1 ：We are given a problem where a car salesman has a probability of 0.05 of selling a car to a customer. We are asked to find the probability that he sells less than 2 cars in a week, given that he sees 13 customers.
Step 2 ：This is a binomial distribution problem. The binomial distribution model deals with finding the probability of success of an event which has only two possible outcomes in a series of experiments. In this case, the two outcomes are selling a car (success) and not selling a car (failure).
Step 3 ：We are asked to find the probability of selling less than 2 cars, which means selling 0 or 1 car. We can use the formula for binomial distribution to solve this problem: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\) where: \(P(X=k)\) is the probability of k successes in n trials, \(C(n, k)\) is the combination of n items taken k at a time, p is the probability of success, and n is the number of trials.
Step 4 ：Given that n = 13 and p = 0.05, we can calculate the probability of selling 0 cars (prob_0) and 1 car (prob_1).
Step 5 ：The probability of selling 0 cars is approximately 0.5133420832795048 and the probability of selling 1 car is approximately 0.3512340569807142.
Step 6 ：The probability of selling less than 2 cars is the sum of the probabilities of selling 0 cars and 1 car, which is approximately 0.864576140260219.
Step 7 ：Final Answer: The probability that the car salesman sells less than 2 cars in a week is approximately \(\boxed{0.865}\).
