Two related experiments are performed. The first has three possible mutually exclusive outcomes: A,B, and C. The second has two possible, mutually exclusive outcomes: X We know P(A) = 0.2 and P(B) = 0.65. We also know the following conditional probabilities if the result of the second experiment is X: P(X|A) = 0.75, P(X|B) = 0.60, and P(X|C) = 0.40. Find P(A|X), P(B|X), and P(C|X). What is the probability that the result of the second experiment is Y?
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Martin Coleman, credit manager for Back's knows that the company uses three methods to encourage collection of delinquent accounts. From past collection records, he learns that 70 percent of the accounts are called on personally 20 percent are phoned, and 10 percent are sent a letter. The probabilities of collecting an overdue amount from an account with the three methods are 0.75, 0.60, and 0.65 respectively Mr. Coleman has just received payment from a past due account. What is the probability that this account.
- Was called on personally?
- Received a phone cal?
- Received a letter?
A public interest group was planning to make a court challenge to auto insurance rates in one of three cities: Atlanta, Baltimore, or Cleveland. The probability that it would choose Atlanta was 0.40, Baltimore, 0.35, and Cleveland, 0.25.
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EconOcon is planning its company picnic. The only thing that will cancel the picnic is a thunderstorm. The Weather Service has predicted dry conditions with probability 0.2, moist conditions with probability 0.45, and wet conditions with probability 0.35. If the probability of a thunderstorm given dry conditions is 0.3, given moist conditions is 0.6, and conditions is 0.8, what is the probability of a thunderstorm? If we know the picnic was indeed canceled, what is the probability moist conditions were in effect?
An independent research group has been studying the chances that an accident at a nucler power plant will result in radiation leakage. The group considers thatthe only possible types of accidents at a reactor are fire, mechanical failure, and human erro, and that two or more accidents never occur together.
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A physical therapist at Enormous State University knows that the football team will play 40 percent of its games on artificial turf this season. He also knows that a football player's chances of incurring a knee injury are 50 percent higher if he is playing on artificial turf instead of grass. If a player's probability of knee injury on artificial turf is 0.42, what is the probability that.
- A randomly selected football player incurs a knee injury?
- A randomly selected football player with a knee injury incurred the injury playing on grass?
The physical therapist from Exercise 4-48 is interested in studying the relationship between foot injuries and position played. His data, gathered over a 3-year period, are summarized in the following table.
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A state Democratic official has decided that changes in the state unemployment rate will have a major effect on her party's chance of gaining or losing seats in the state sente. She has determined that if unemployment rises by 2 percent or more, the respective probabilities of losing more then 10 seats, losing 6 to 10 seats, gaining or losing 5 or fewer seats, gaining 6 to 10 seats, and gaining more than 10 seats are 0.25,0.35, 0.15, 0.15, and 0.10, respectively. If unemployment changes by less than 2 percent, the respective probabilities are 0.10, 0.10, 0.15, 0.35, and 0.30.
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T.C Fox, marketing director for Metro-Goldmine Motion pictures, believes that the studio's upcoming release has a 60 percent chance of being a hit, a 25 percent chance of being a moderate success, and a 15 percent chance of being a flop. To test the accuracy of his opinion, T>C> has scheduled two test screenings. After each screening, the audience rate the film on a scale of 1 to 10, 10 being best.
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"The chance of rain today is 80 percent." Which of the following best explains this statement?
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