2. Hashir is going to graduate from an industrial engineering department in a university by the end of the semester. After being interviewed at two companies he likes, he assesses that his probability of getting an offer from company A is 0.8, and his probability of getting an offer from company B is 0.6. If he believes that the probability that he will get offers from both companies is 0.5, what is the probability that he will get at least one offer from these two companies?

In 2013, the total sales from 3 different car production companies was 606,334 cars or light trucks. The probability that the vehicle was made by Company A was 0.386, by Company B 0.350, and by Company C 0.258. Additionally, the probability that a Company A vehicle sold was a car was 0.379, a Company B vehicle sold was a car was 0.370, and a Company C vehicle sold was a car was 0.332. Given the vehicle sold was a car, find the probability it was made by Company A. The probability a vehicle was made by Company A, given it was a car is (Round to three decimal places as needed.)

You are an analyst for a consumer products company. You run a survey of 1000 customers and find that 80% of customers use gel packs for laundry detergent (the rest use liquid or powder) and 40% of customers use gel packs for their dishwasher detergent (the rest use liquid or powder). You also learn that twice as many customers use laundry detergent than dishwasher detergent.

A door-to-door salesman expects to make a sale 14% of the time when starting the day. But making a sale increases his enthusiasm so much that the probability of a sale to the next customer is 0.39. If he makes no sale, the probability for a sale to the next customer stays at 0.14. What is the probability that he will make at least two sales with his first three visits?