form 3 probability

Fung

2009-08-14 5:17 am

In oeder to play a game, all participanys need to pay $10 in advance. Each participant needs to draw twice from a bag containing 1 red ball and 4 white balls with replacement. If two re balls are drawn, the participant will gain $100. If the colours of the two balls are different, the participany will gan $20. If two white balls are drawn, the participant will lose $1.

a) Find the probability that the colours of the two balls drawn are different.

b) Find the probability that the colours of the two balls drawn are same

c) Mr.Chan says that participants can gain money in playing the game. Do you agree? Explain your answer.

回答 (1)

Prof. Physics

2009-08-14 5:24 am

✔ 最佳答案

a. P(colours of the two balls are different)

= P(1st ball is red) X P(2nd ball is white) + P(1st ball is white) X P(2nd ball is red)

= 1/5 X 4/5 + 4/5 X 1/5

= 8/25

b. There are two methods.

i. P(two balls are same)

= P(1st and 2nd are white) + P(1st and 2nd are red)

= 4/5 X 4/5 + 1/5 X 1/5

= 17/25

ii. P(two balls are same)

= 1 - P(two balls are different)

= 1 - 8/25

= 17/25

ii. P(two balls are white)

= 4/5 X 4/5

= 16/25

P(two balls are red) = P(two balls are same) - P(two balls are white)

= 17/25 - 16/25

= 1/25

Expected gain of the player

= 100(1/25) + 20(8/25) + (-1)(16/25) - 10

= $-0.24

So, I do not agree that the participants can gain money from the game.

參考: Physics king

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