F.5 math's probability

呢啲加奶

2013-03-27 4:37 am

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)

回答 (1)

myisland8132

2013-03-27 5:20 am

✔ 最佳答案

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

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