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