高考M&S prob.一問!!!

2011-12-26 7:59 am

a room attendant of a hotel with 20 rooms has 2 master keys, each of which can open 10 rooms. in a morning , 5 of the rooms have already een unlocked for cleaning. the room attdant wants to enter one of the 20 rooms. if she just picks one master key at random, what is the probability that she will be able to enter the room?

回答 (1)

用戶2053

2012-02-05 9:10 am

✔ 最佳答案

P(she will be able to enter the room)

= P(5 of choosen key rooms unlocked) * (10/20)
+ P(4 of choosen key rooms unlocked) * (11/20)
+ P(3 of choosen key rooms unlocked) * (12/20)
+ P(2 of choosen key rooms unlocked) * (13/20)
+ P(1 of choosen key rooms unlocked) * (14/20)
+ P(0 of choosen key rooms unlocked) * (15/20)

= (5C5)(1/2)⁵ (10/20)
+ (5C4)(1/2)⁵ (11/20)
+ (5C3)(1/2)⁵ (12/20)
+ (5C2)(1/2)⁵ (13/20)
+ (5C1)(1/2)⁵ (14/20)
+ (5C0)(1/2)⁵ (15/20)

= (1/640) (10 + 5*11 + 10*12 + 10*13 + 5*14 + 15)

= 5/8

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