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標題:

F.5 math's probability

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發問:

1. Events E and F are independent events. It is given that P(E) = 0.6 and P(F) = 0.9. Find P(E or F). (Ans: 0.96)2. Peter and John take turns to throw a fair dice. The one who can get a '6' firstwill win the game. If the game starts woth Peter, find the probabilities that (a) Peter... 顯示更多 1. Events E and F are independent events. It is given that P(E) = 0.6 and P(F) = 0.9. Find P(E or F). (Ans: 0.96) 2. Peter and John take turns to throw a fair dice. The one who can get a '6' first will win the game. If the game starts woth Peter, find the probabilities that (a) Peter wins in the second round, (Ans:25/216) (b) there is a winner in the second round. (Ans:275/1296) 3. The Police Department has just purchaed a new a lie detector. The officer performed a test run by asking volunteers some questions. The results are recorded in the following table. Detector indicates truth: Volunteer tells the truth (85) Volunteer lies(7) Detector indicates lie: Volunteer tells the truth (15) Volunteer lies(93) Estimate the following based on th eabove data. If the probabilty that Ernest lies is 1/10, what is the probabilty that the detector indicates correctly? (Ans:429/500)

最佳解答:

1 P(E OR F) = P(E) + P(F) - P(E)P(F) = 0.6 + 0.9 - 0.6 * 0.9 = 1.5 - 0.54 = 0.96 2(a) P(Peter wins in the second round) = 5/6 * 5/6 * 1/6 = 25/216 (b) P(There is a winner in the second round) = 5/6 * 5/6 * 1/6 + 5/6 * 5/6 * 5/6 * 1/6 = 275/1296 3 P(detector indicates correctly) = P(detector correct | Ernest tells the truth) P(Ernest tells the truth) + P(detector correct | Ernest lies) P(Ernest lies) = 85/92 * 9/10 + 93/108 * 1/10 = 765/920 + 93/1080 = 0.91763285

其他解答:5FAD1C75CFAE8A5F