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 even) = P𝑃 (sum is 3) = P𝑃 (sum is 10) =
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 even) = P𝑃 (sum is 3) = P𝑃 (sum is 10) =
Solution
To solve this problem, we first need to understand that when rolling two dice, there are a total of 36 possible outcomes (6 outcomes for the first die multiplied by 6 outcomes for the second die).
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P(sum is even): An even sum can be obtained in several ways (1+1, 1+3, 1+5, 2+2, 2+4, 3+1, 3+3, 3+5, 4+2, 4+4, 5+1, 5+3, 5+5, 6+2, 6+4, 6+6). There are 18 such combinations. So, the probability is 18/36 = 1/2.
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P(sum is 3): A sum of 3 can only be obtained in two ways (1+2, 2+1). So, the probability is 2/36 = 1/18.
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P(sum is 10): A sum of 10 can be obtained in three ways (4+6, 5+5, 6+4). So, the probability is 3/36 = 1/12.
So, the probabilities are:
P(sum is even) = 1/2 P(sum is 3) = 1/18 P(sum is 10) = 1/12
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