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arabie
04-22-2005, 12:21 AM
A fair die is rolled 200 times. What is the probability that a five or a six shows up less than 25% of the time?

arabie
04-22-2005, 10:13 PM
bump. common someone has to know the answer!

Precision1C
04-22-2005, 11:26 PM
The answer is a summation of the chances of N=0 to 49 times that a 5 or a 6 is rolled.

The formula for any N between 0 and 200 is F(N)=[200!/(N!*(200-N)!)](1/3)^N*(2/3)^(200-N)]

So use this formula to determine F(N) for N=0 to 49 and then add them up and voila you are done. This isn't a hard problem just very tedious.

BruceZ
04-23-2005, 02:28 AM
[ QUOTE ]
A fair die is rolled 200 times. What is the probability that a five or a six shows up less than 25% of the time?

[/ QUOTE ]

Using Excel =BINOMDIST(49,200,1/3,TRUE) = 0.42%.

This gives the exact answer.

Or using the normal approxmimation:

sigma = sqrt[200*(1/3)*(2/3)] = 6.67.

49 is 2.64 sigma below the average of 66.67, corresponding to 0.41%.