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Discrete Math

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You are stranded on a deserted island, and along the way you stumble across a genie. He says he will get you off the island provided that you can meet his conditions. He hands you a 20-sided die, and says that you need to roll it 1000000 (one million) times. If you can roll between 100000 and 100005 rolls of the numbers 8 – 10, he will teleport you off this island. Otherwise you are stuck here. What is the probability you will roll between 100000 – 100005 rolls of the numbers 8 – 10 while rolling the die 1000000 times?

Im afraid you are stuck, the probability is too small to calculate.
This is a simple binomial distribution problem; either you roll an 8,9,10 or you dont. The probability of yes is 3/20 = .15 So, with 1M rolls, the expected mean 8-10 is 150000, with a standard deviaiton of sqrt(.15*.85*1000000) = 357. Since 100,000 is 5000 rolls or 14 standard deviations away from the mean, there is virtually no chance.

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