If the outcome of event A is not affected by event B, then events A and B are said to be   dependent   not mutually exclusive   independent   mutually exclusive

If A and B are events which are conditionally independent given a third event C, which of the following is not necessarily true? Select one: O a. P(An B|Cº) = 1 – P(A|C)P(B|C) O b. P(BANC) = P(B|C) O c. None of the other choices d. P(An B|C) = P(A|C) – P(A|C)P(Bª|C) O e. P(An BnC) = P(A|C)P(BC)

Which of the following statements is false?    Two independent events cannot occur at the same time.   Two complementary events cannot occur at the same time.   Two disjoint events cannot occur at the same time.

Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A₁ be the event that the receiver functions properly throughout the warranty period, A₂ be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A₁) = 0.92, P(A₂) = 0.96, and P(A3) = 0.90. (Round your answers to four decimal places.) (a) What is the probability that all three components function properly throughout the warranty period? (b) What is the probability that at least one component needs service during the warranty period? (c) What is the probability that all three components need service during the warranty period? (d) What is the probability that only the receiver needs service during the warranty period? (e) What is the probability that exactly one of the three components needs service…

a and b

Suppose there are exactly three states of weather: sunny, cloudy, or rainy. If it is sunny today, then the probability is 3/4 that it will be sunny tomorrow, 1/8 that it will be cloudy tomorrow, and 1/8 that it will be rainy. If it is cloudy today, then the probability is 1/2 that it will be sunny tomorrow, 1/4 that it will be cloudy tomorrow, and 1/4 that it will be rainy. If it is rainy today, then the probability is 1/4 that it will be sunny tomorrow, 1/2 that it will be cloudy tomorrow, and 1/4 that it will be rainy. cloudy is From this Markov model, for any given day the probability that it will be sunny is rainy is Round your answers to three decimal places. and

ABC Airlines' first class cabins have 10 seats in each plane. ABC's overbooking policy is to sell up to 11 first class tickets, since cancellations and no-shows are always possible (and indeed are quite likely). For a given flight on ABC Airlines, there were 11 first class tickets sold. Suppose that each of the 11 persons who purchased tickets has a 20% chance of not showing up for the flight, and that the events that different persons show up for the flight are independent. (Please assume that there is no refund if the customer does not show up for the flight) (a) What is the probability that at most 5 of the 11 persons who purchased first class tickets show up for the flight? (b) What is the probability that exactly 10 of the 11 persons who purchased first class tickets show up for the flight? (c) Suppose that the cost of each first class ticket is $12,000. (Let's assume that this $12,000 contributes entirely to profit since the variable cost associated with a passenger on a flight…