Discuss the below:
Q1. The Happy Valley Machine Works Company loses a shipment of its machines due to an error by one of its three executives (Harry, Sam and Mabel), but it cannot tell with certainty which executive was responsible for the error. On the basis of past performance, it is known that the probability that Harry would make such a mistake (given that he were responsible for the shipment) is 0.05, the probability that Sam would do so is 0.15 and that Mabel would do so is 0.10. If Harry is responsible for 50% of all shipments and the rest are split evenly between Mabel and Sam, what is the probability that Sam is responsible for the lost shipment?
Q2. For their market research project, Sam and Mary are surveying firms in their area. They ask each firm how many of their workers carpool and how many are at least 40 years old. They have received the following information about 75 coworkers
20 of the car-poolers are at least forty years old
15 of the car-poolers are younger than forty
35 of the workers are at least forty years old
25 of the workers who do not carpool are less than forty
a) Construct the probability matrix for this data
b) What is the probability that a worker chosen at random who does not carpool is at least 40 years old? Explain whether a worker's age and her carpooling status are statistically independent.