概率問題 15POINTS

2010-03-09 10:09 pm
1)一個男人有10條KEYS,其中兩條KEYS CAN OPEN THE DOOR.他隨意CHOOSE出一條KEY來試開大門,在不把KEY放回的情況下,直至能把大門打開為止.求他最少需要經過3次嘗試後,才能OPEN THE DOOR 的PROBABILITY



2 ) what is the probability that a 2-digit number chosen at random is divisible by 11

回答 (2)

2010-03-09 10:16 pm
✔ 最佳答案
1) P(最少需要經過3次嘗試後,才能OPEN THE DOOR)
= P(第一及第二次不能OPEN THE DOOR)
= (8/10)(7/9)
= 28/45
2) 11 , 22 , 33 , 44 ,55 , 66 , 77 , 88 , 99 from 10 - 99
9 numbers from 99 - 9 = 90 numbers
P(a 2-digit number chosen at random is divisible by 11)
= 9/90
= 1/10
2010-03-10 2:39 am
1) 最少需要經過3次嘗試既互補事件 :
第一次成功+第二次才成功
(2/10)+(8/10)*(1/9)
=13/45
P(最少需要經過3次嘗試)= 1 - 13/45
= 32/45

2 )P(divisible by 11) = 9/90
=1/10


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