You are playing a game where you must roll two 4 sided dice each die can yield a value of 1 2 3 or 4 The goal is to obtain a

Question

You are playing a game where you must roll two 4 sided dice each die can yield a value of 1 2 3 or 4 The goal is to obtain a score of at least 6 You initially roll both dice and are allowed to reroll one of them the other die value must be kept For example if you roll the dice and obtain the results of 1 and 3 you will want to reroll the die with a value of 1 to try to get a higher value You do not need to roll again if your initial roll obtains a combined score of at least 6 Find the following a The probability that you succeed without needing to reroll the dice the odds that the values sum to at least 6 when you first roll both dice b In what scenario would you be unable to succeed after your first roll think what values must be present on both dice in which rerolling one of them will never allow them to sum to at least 6 What is the likelihood of this c You discover that one of the die is rigged and will always roll a 2 Given this information what is the chance of each of the following i You succeed in any given turn your chance to obtain a total score of 6 or greater given the initial rules ii After 5 tries you succeed at least 3 times iii You succeed exactly 5 times after 7 tries

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