1. Jack and Diane are applying to work at the Tasty Freeze Ice Cream Parlor, After interviewing them, the manager says, " The probability that I hire Jack is 0.7 and the probability that I hire Diane is 0.4. The probability that I hire at least one of you is 0. 9. " What is the probability that both Jack and Diane get hired?

2. True or False: If two events are independent, then they must be mutually exclusive. Explain.

3. Assume that 70% of teenagers who go to take the written driver's license test have studied for the test. Of those who study for the test, 95% pass; of those who do not study for the test, 60% pass. What is the probability that a teenager who passes the written driver's license test did not study for the test?

4. A system has two components that operate in parallel, as shown in the diagram below. Because the components operate in parallel, at least one of the components must function properly the system is to function properly. Let F denote the event that component 1 fails during one period of operation and G denote the event that component 2 fails during one period of operation. Suppose P( F) =0.20 and P( G) = 0. 03. The component failures are independent. What is the probability that the system functions properly during one period of operation?