F.6 maths(2Q)

2010-03-31 7:46 am

1. An unbiased coin is tossed 3 times. What is the probability of getting
a) 3 tails
b) 1 head and 2 tails
c) at least 1 head

2. If two dice are thrown, find the probability of rolling a sum
a) equal 8?
b) equal 13?
c) smaller than 10?

回答 (2)

用戶2053

2010-03-31 8:07 am

✔ 最佳答案

1a)
(1/2)^3 = 1/8
1b)
P(HTT) + P(THT) + P(TTH) = 3 x (1/3)^3 = 1/9
or
(1/3)^3 x 3!/2! = 1/27 x 3 = 1/9
1c)
1 - P(TTT)
= 1 - (1/3)^3
= 26/27
2a)
P(1 , 7) + P(7 , 1) + P(2 , 6) + P(6 , 2) + P(3 , 5) + P(5 , 3) + P(4 , 4)
= 7 x (1/6)^2
= 7/36
2b)
The maximum value is 6 + 6 = 12 , equal 13 is impossible.
P(equal 13) = 0
2c)
= 1 - P(greater than 10)
= 1 - P(5 , 6) - P(6 , 5) - P(6 , 6)
= 1 - 3 x (1/6)^2
= 1 - 1/12
= 11/12

2010-03-31 00:16:25 補充：
Corrections 1b) (1/3) should be (1/2) :

1b)

P(HTT) + P(THT) + P(TTH) = 3 x (1/2)^3 = 3/8

or

(1/2)^3 x 3!/2! = 1/8 x 3 = 3/8

1c)

1 - P(TTT)

= 1 - (1/2)^3

= 7/8

2010-03-31 00:19:47 補充：
2c)

= 1 - P(greater than 10) - P(equal to 10)

= 1 - P(5 , 6) - P(6 , 5) - P(6 , 6) - P(5 , 5)

= 1 - 4 x (1/6)^2

= 1 - 1/9

= 8/9

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[匿名]

2010-04-04 3:10 am

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