Probability

Question

While playing Yahtzee, Amanda rolls five dice and gets a 1, a 2, a 4, a 5, and a 6. She decides to keep the 1,2, and 4, and reroll the 5 and 6. What is the probability that Amanda will have a small straight(1-2-3-4 plus anything else) or a pair of 3's?

Answer 1

If Amanda gets a pair of 3's by rolling double 3's with the reroll then she will get a small straight as well, so we need only find the probability that Amanda rolls at least one 3 with the two dice she rerolls.  

 

There are 11 rolls of two dice that have at least one 3, they are 

 

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6) 

(1,3), (2,3),        , (4,3), (5,3), (6,3) 

 

There are 6*6 = 36 possible rolls with two dice, so the probability of at least one 3 with two dice rerolled is 

 

11/36 ~ 0.3056