Below is a list of all possible outcomes in the experiment of rolling two die.Note: The table gives the values of each die, not the sum of the two die.Determine the following probabilities. Write your answers as reduced fractions.P𝑃(sum is 12) = P𝑃(sum is 8) = P𝑃(sum is 4) =
Question
Below is a list of all possible outcomes in the experiment of rolling two die.Note: The table gives the values of each die, not the sum of the two die.Determine the following probabilities. Write your answers as reduced fractions.P𝑃(sum is 12) = P𝑃(sum is 8) = P𝑃(sum is 4) =
Solution
To determine the probabilities, we first need to understand that there are 36 possible outcomes when rolling two dice (6 outcomes for the first die multiplied by 6 outcomes for the second die).
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P(sum is 12): The only way to get a sum of 12 is to roll a 6 on both dice. So there is only 1 favorable outcome. Therefore, the probability is 1/36.
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P(sum is 8): The pairs that sum to 8 are (2,6), (3,5), (4,4), (5,3), and (6,2). So there are 5 favorable outcomes. Therefore, the probability is 5/36.
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P(sum is 4): The pairs that sum to 4 are (1,3), (2,2), and (3,1). So there are 3 favorable outcomes. Therefore, the probability is 3/36, which reduces to 1/12.
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