F3 MATHS!!!!!!!!!!!!!!!!!!!!

2006-12-09 6:44 am

f.3 maths ~~~~~~~~
In a dice game,the player first pays $10for the game and then tosses two dice.If the sum of the numbers shown is greater than or equal to 9,the player will be reward with $20,otherwise the player will be rewarded with $n.

(a)if n=2,what is the expected reward for the player?Is the game fair to the player?Why?

(b) find,correct to the nearest integer,the least value of n such tht the game is more favourable to the player.

回答 (1)

vsloy

2006-12-09 8:02 am

✔ 最佳答案

For 2 dice, there are 6² = 36 combinations.
10 of them are greater than or equal to 9.
(3-6, 4-5, 5-4, 6-3, 4-6, 5-5, 6-4, 5-6, 6-5 & 6-6)
Therefore, the chance is 10/36 = 5/18
And the expected reward for the game is:
　5/18*20 + (1-5/18)*n
(a) If n=2, the expected reward will be:
　5/18*20 + (1-5/18)*2 = 126/18 = 7
　The game is not fair to the player ($7),
　since the expected reward is less than what he paid ($10).
(b) If the game is more favourable to the player,
　that means the expected reward is more than $10.
　5/18*20 + (1-5/18)*n ＞ 10
　　　　　　(13/18)*n ＞ 80/18
　　　　　　　　　　n ＞ 80/13
　　　　　　　　　　n ＞ 6-2/13
　Therefore, the least value of n such that the game is more favourable
　to the player is 7 (correct to the nearest integer).

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