1. A computer hacker has 9 passwords to break into several HSBCC bank computers. Only 1 password will open all of the HSBCC bank computers. If 25% of these HSBCC bank computers are usually left unlocked, what is the probability that the computer hacker can get into a specific HSBCC bank computer if the computer hacker selects 5 passwords at random before trying them?

2. Googley phone company uses three phone manufacturers to make their phones. For cost reasons, all three manufacturers are used at varying times. In fact, manufacturers 1, 2, and 3 are used for 23%, 37%, and 40% of the time to make their phones, respectively.

Given that P(D|M1) = 0.12, P(D|M2) = 0.08, P(D|M3) = 0.06,

where P(D|Mj ) is the probability of a defective phone, given that it was made by manufacturer j. If a random Googley phone was observed and found to be defective, which manufacturer (1, 2 or 3) most likely manufactured the phone? Please justify your answer.