Bunuel wrote:

Paul is playing a game wherein he rolls a 6-sided die. If the number on the die is even, he gains a point and continues to roll. If it is odd and prime, he stops and keeps the double the number of points that he has gained. If it is odd but not prime, he must stop rolling and keeps all of his points. What is the probability that Paul gets exactly 4 points?

A. 1/96

B. 1/12

C. 1/16

D. 3/32

E. 7/48

IMO

Option DGiven : {2,4,6} -> + 1 Point

{3,5} -> Double of existing points

{1} -> Stop and retain existing points

To Find : Probability of getting 4 points.

Solution :

Ways to get 4 points 1) Throw either of {2,4,6} 4 times followed by {1} to stop.

P(selecting {2,4,6}) = 1/2

P(selecting {1}) = 1/6

->\(\frac{1}{2}*\frac{1}{2}\)*\(\frac{1}{2}*\frac{1}{2}*\frac{1}{6}\) =

\(\frac{1}{96}\)2) Throw either of {2,4,6} 2 times followed by either {3,5} to double points and then stop.

P(selecting {2,4,6}) = 1/2

P(selecting {3,5}) = 1/3

->\(\frac{1}{2}*\frac{1}{2}*\frac{1}{3}\)=

\(\frac{1}{12}\)P(Getting score 4 ) = \(\frac{1}{96} + \frac{1}{12}\) = \(\frac{3}{32}\)

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Regards ,

Dhruv

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