a. What is the probability of rolling a large straight (either 1-2-3-4-5 or 2-3-

Question

a. What is the probability of rolling a large straight (either 1-2-3-4-5 or 2-3-4-5-6) on one roll of the five dice? b. Given that two 6's have been rolled, what is the probability that one more roll of the remaining three dice will yield at least one more six? c. The probability of throwing five 1's (called a Yahtzee in 1's) on exactly two (its, what throws IS_ -1. Suppose you know that five 1's were thrown in 6 exactly two throws. What is the probability that four 1's occurred on the first throw? (Hint: Use Bayes' theorem.)

Explanation / Answer

a.)

The probability of rolling 1-2-3-4-5 in that order is (1/6)5 However any order will do, so it's 5!(1/6)5.

The probability of rolling 2-3-4-5-6 is similarly 5!(1/6)5

Combining, we get 240(1/6)5 0.03, i.e. about 3% of the time.

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