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# Probability

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A standard six-sided die is rolled twice. What is the probability that the product of the rolls is 1, 2, or 3?

Mar 10, 2023

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To get a product of 1 with two dice rolls, we must roll a 1 on the first die and a 1 on the second die.

To get a product of 2, we can either roll a 1 on the first die and a 2 on the second die, or roll a 2 on the first die and a 1 on the second die.

To get a product of 3, we can either roll a 1 on the first die and a 3 on the second die, or roll a 3 on the first die and a 1 on the second die.

So, the possible outcomes that give us a product of 1, 2, or 3 are:

Rolling a 1 on the first die and a 1 on the second die

Rolling a 1 on the first die and a 2 on the second die

Rolling a 2 on the first die and a 1 on the second die

Rolling a 1 on the first die and a 3 on the second die

Rolling a 3 on the first die and a 1 on the second die

This gives us a total of 5 possible outcomes out of 36:

(1, 1)

(1, 2)

(2, 1)

(1, 3)

(3, 1)

Therefore, the probability of getting a product of 1, 2, or 3 is:

P(product = 1, 2, or 3) = 5/36

So the probability of getting a product of 1, 2, or 3 is 5/36.

Mar 11, 2023