Which of the following is the sample space for this random experiment?

1. Let A and B be two disjoint events such that P(A) = .20 and P(B) = .60.

What is P(A and B)?

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0 .12 .68 .80 None of the above.

2. In the population, 8% of males have had a kidney stone, while only 2% of females have had a kidney stone. Suppose a medical researcher randomly selects one male and one female from the population.

Let A represent the event “the selected male has had a kidney stone.”

Let B represent the event “the selected female has had a kidney stone.”

Which of the following is true about the two events?

A and B are disjoint. A and B are independent. A and B are complements. All of the above are true. Only (A) and (B) are true. None of the above is true. I thought only A and B were true, but I was wrong…

3. For safety reasons, four different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the four systems detects theft with a probability of .99 independently of the others. The bank, obviously, is interested in the probability that when a theft occurs, at least one of the four systems will detect it. This probability is equal to:

(.99)4 (.01)4 1 – (.01) * 4 1 – (.99)4 1 – (.01)4 (that’s an exponent 4, not a regular 4) I’m guessing the answer is the last one.

4. A coin is tossed three times, or until the first “heads” appears, whichever occurs first. Which of the following is the sample space for this random experiment?

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} S = {H, TH, TTH} S = {H, TH, TTH, TTT} S = {H, HH, HHH} S = {H, HT, HHT, HHH} I thought the answer was the second option there, but it told me I was wrong…