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