Question

A bar has a dice game that works as follows: You simultaneously roll 5 dice, and...

A bar has a dice game that works as follows: You simultaneously roll 5 dice, and if all 5 dice are the same value, you win. If your dice are not all the same, you get to re-roll all 5 dice again. You get three tries in total. What is the probability of winning? That is, what is the probability that in your three tries, at least one of your rolls consists of five-of-a-kind?

Math   Statistics-And-Probability   
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Answer #1

Probability of getting 1 in all 5 dice is 1/6*1/6*1/6*1/6*1/6 = 1/6^5

Probability of getting 2 in all dice = 1/6^5

Similarly probability of getting 3,4,5,6 in all 5 dice is also 1/6^5

So total probability of winning in a single throw is 6/(6)^5 = 1/6^4

Probability of losing is 1-1/6^4

Now according to problem we have 3 throws

Probability of atleast on throw getting same numbers is = 1- probability of not getting all same numbers in any throw

= 1- 3C0(1/6^4)^0*(1-1/6^4)^3 = 0.0023

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