中五數學問題-概率 - Ans.fyi 參考答案

中五數學問題-概率

2009-01-05 8:35 am

Mike and Ken are throwing two darts at a target respectively.In every
shot,the probability that Mike hits the target is "3/5" while that for
Ken is "1/4". If one point for a dart is hit and no point for a dart
is missed,find the probability that

(a)Mike gets 1 Point
(b)Ken gets 1 Point
(c)Mike and Ken get equal points
(d) Ken gets a higher point than Mike

回答 (1)

用戶8785

2009-01-05 9:30 am

✔ 最佳答案

P(Mike gets 1 point) = 3/5 x 2/5 + 2/5 x 3/5
= 6/25 x 2
= 12/25
Qb)
P(Ken gets 1 point) = 1/4 x 3/4 + 3/4 x 1/4
= 3/16 x 2
= 3/8
Qc)
P(Mike and Ken get equal points)
= P(both get 2 points) + P(both get 1 point) + P(both get 0 point)
= ( 3/5 x 3/5 x 1/4 x 1/4 ) + ( 12/25 x 3/8 ) + ( 2/5 x 2/5 x 3/4 x 3/4)
= 9/400 + 72/400 + 36/400
= 117 / 400
Qd)
P(Ken gets higher point than Mike)
= P(Ken=2, Mike=1) + P(Ken=2, Mike=0) + P(Ken=1, Mike=0)
= ( 3/5 x 3/5 x 3/8 ) + ( 3/5 x 3/5 x 3/4 x 3/4 ) + ( 12/25 x 3/4 x 3/4 )
= 27/200 + 81/400 + 108/400
= 243 / 400

參考: myself... 嚴禁抄襲

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