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Ps - Probablity

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Senior Manager
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Ps - Probablity [#permalink]

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New post 05 Jan 2006, 04:21
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Find the probability of getting a larger number than the previous number every time, when an unbiased die is thrown three times.

(a) 1/18 (b) 15/216

(c) 25/216 (d) 5/54

Please show your workings.
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New post 05 Jan 2006, 04:47
Possibilites:

First throw is 1: 2,3 - 2,6; 3,4 - 3,6; 4,5 - 4,6; 5,6 --> Total: 10 ways

First throw is 2: 3,4 - 3,6; 4,5 - 4,6, 5,6 --> Total: 6 ways

First throw is 3: 4,5 - 4,6, 5,6 --> Total: 3 ways

First throw is 4: 5,6 -> Total: 1 ways

First throw is 5: No way

First throw is 6: No way

Total number of possibilites = 20

Total number of combinations with three rolls of a die = 6*6*6 = 216

Probability = 20/216 = 10/108 = 5/54 (D)

P.S: This method may not look elegant, but it's extremely fast.
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New post 07 Jan 2006, 00:55
5/54..

Here's my working

Prob of getting a number on the first throw= 1/6

Prob of getting a no higher on the second throw = 5C1/6 ( Only 5 nos r left)=5/6

Prob of getting a no higher than 3rd throw= 4C1/6 (Only 4 r left_=4/6

1/6*5/6*4/6=5/54
  [#permalink] 07 Jan 2006, 00:55
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