A company has 3 factories (factory 1, factory 2 and factory 3) that manufacture the same chip. Each produces 15%, 35% and 50% of the total production. The probability that the manufacturing chip is defective from factories 1,2 and 3 are 0.01, 0.05, and 0.02, respectively. Suppose then that someone finds a manufacturing defect in the chip, what is the probability that the defective chip came from factory 1?

Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Pedro make it to their first period class on time is 0.29.  The probability that Napoleon and Pedro catch the bus is 0.87. However, the probability that they make it to their first period class on time, given that they catch the bus is 0.81.  What is the probability that Napoleon and Pedro catch the bus and make it to their first period class on time?

Suppose that historically, 35% of applicants that are offered admittance to Texas Tech actually enroll, while the others take offers somewhere else. If Texas Tech will accept 9000 this coming year, what is the probability that less than 34.1654% will actually enroll?

Suppose that if person with tuberculosis is given a TB screening, the probability that his or her condition will be detected is 0.90. If a person without tuberculosis is given a TB screening , the probability that he or she will be diagnosed incorrectly as having tuberculosis is 0.3. Suppose, further, that 11% of the adult residents of a certain city have tuberculosis. If one of these adults is diagnosed as having tuberculosis based on the screening, what is the probability that he or she actually has tuberculosis?

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?

Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Pedro make it to their first period class on time is 0.30.  The probability that they make it to their first period class on time, given that they catch the bus is 0.90.  The probability that Napoleon and Pedro catch the bus and make it to their first period class on time is 0.21.  What is the probability that Napoleon and Pedro catch the bus?