f.5 Probability 問題

[匿名]

2009-12-13 1:54 am

1. In a game, the probabilities that A and B win a prize are 1/3 and 2/3 respectively. If they play game once, find the probability that either A or B wins the game.

點解個答案係 7/9?

2. The probabilities that Peter will be late for school on a school day is 0.4 if he travels by bus and0.2 if he travels by KCR. Given that the probabilities that Peter travels by bus and KCR are the same, find the probability that Peter will not be late for school in the three consecutive school days.

點解個答案係 0.343?

3. In a test, there are four multiple choice questions. Each question has 4 choices, only one of which is correct. In order to pass the test, John should at least answer two questions correctly. Find the probability that John can pass the test if he answer the questions by wild guessing.

點解個答案係 67/256 ?

請問有邊個識? 如果識，可以教我嗎?

回答 (1)

Prof. Physics

2009-12-13 2:12 am

✔ 最佳答案

1. P(either A or B win after one game)

= 1 - P(either A or B win at the first round)

= 1 - (1 - 1/3)(1 - 2/3)

= 1 - (2/3)(1/3)

= 7/9

2. P(Peter will not be late)

= P(Peter takes bus and not late) + P(Peter takes KCR and not late)

= 0.5(1 - 0.4) + 0.5(1 - 0.2)

= 0.5(0.6) + 0.5(0.8)

= 0.7

P(Peter will not late for 3 consecutive days)

= (0.7)^3

= 0.343

3. P(John can pass the test)

= P(John has two correct answers or more)

= 4C2 (1/4)(1/4)(1 - 1/4)(1 - 1/4) + 4C3 (1/4)^3(1 - 1/4) + (1/4)^4

= 67/256

參考: Physics king

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