Math Problem Statement
The game of Yahtzee is played with five fair dice. The goal is to roll certain ‘hands’, such as Yahtzee (all five dice showing the same number) or a full house (three of a kind and two of a kind). In the first round of a player’s turn, the player rolls all five dice. Based on the outcome of that roll, the player has a second and third round, where he/she can then choose to re-roll any subset of the dice to get a desired hand. Suppose that, on the second round, the dice are {2, 3, 4, 6, 6}. You decide to re-roll both sixes in the third round. What is the probability that you roll either a small straight (exactly four dice are in a row) or a large straight (exactly five dice are in a row)? Round your answer to three decimal places.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Combinatorics
Formulas
Probability of desired outcomes / Total possible outcomes
Theorems
Basic Probability Theory
Suitable Grade Level
Grades 10-12
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