Rolling a 6 six times
Probability
Level
3
A die is rolled until 6 appears 6 times. What is the probability that this happens on the 36th roll? Give your answer correct to 3 significant figures.
The answer is 0.0293.
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1 solution
Let X be the discrete random variable "number of trials to get 6 six times." Therefore, X follows the Negative Binomial Distribution with r = 6 (the fixed number of successes) and p = 1/6 (the constant and independent probability of success).
Using the Probability Distribution Function for the Negative Binomial Distribution, we have that:
P(X = 36) = 35C5 x ( 6 1 ) ^6 x ( 6 5 ) ^30 = 0.0293