A construction firm bids on two different contracts. Let E, be the event that the bid on the first contract is successful, and define E, analogously for the second contr Suppose that P(E₁) = 0.6 and P(E₂) = 0.7 and that E₁ and ₂ are independent events. (a) Calculate the probability that both bids are successful (the probability of the event E₁ and ₂). (b) Calculate the probability that neither bid is successful (the probability of the event (not E₁) and (not E₂)). (c) What is the probability that the firm is successful in at least one of the two bids?

Assume that the probability that an airplane engine will fail during a torture test is 12and that the aircraft in question has 4 engines. Construct a sample space for the torture test. Use S for survive and F for fail.

If the spinner shown below is spun, find the probability of each event. Assume that the spinner never stops on a line. The spinner stops on orange.

Smokers and Non smokers In a population of 10,000, there are 5000 non-smokers, 2500 smokers of one pack or less per day. During any month, there is a 5 probability that a nonsmoker will begin smoking a pack or less per day, and a 2 probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10 probability of quitting and a 10 probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 5 probability of quitting and a 10 probability of dropping to a pack or less per day. How many people will be in each group a in 1 month, b in 2 months, and c in 1 year?