Discrete Probability Distributions — Grinstead & Snell
Mathematics — Probability · simulation-discrete-probabilities
Problem
Consider the bet that all three dice will turn up sixes at least once in n rolls of three dice. Calculate f(n), the probability of at least one triple-six when three dice are rolled n times. Determine the smallest value of n necessary for a favorable bet that a triple-six will occur when three dice are rolled n times. (DeMoivre would say it should be about 216log2=149.7 and so would answer 150---see Exercise 1.2.17. Do you agree with him?)