Two dice are rolled. Find the probability that a multiple of three is rolled on one die and an even number is rolled on the second die.

for the even number:3/6. i'm not so sure if you have to reduce this to lowest terms.

3 and 6 are multiples of 3. The probability the either one or the other events would occur is obtained by adding the probability of the individual events. Probability = 1/6 + 1/6 = 2/6 = 1/3

2, 4 and 6 are even numbers = 1/6 + 1/6 + 1/6 = 3/6 = 1/2

The probability that both/all events would occur is found by multiplying the probability of the individual events.

I hope this helps. Thanks for asking.

To find the probability of two independent events occurring together, we need to multiply the probabilities of each individual event.

Let's consider the first die. A multiple of three can be rolled on a die in 2 out of the 6 possible outcomes. Therefore, the probability of rolling a multiple of three on the first die is 2/6, which simplifies to 1/3.

Now let's move on to the second die. To roll an even number, there are 3 favorable outcomes (2, 4, and 6) out of the 6 possible outcomes. Therefore, the probability of rolling an even number on the second die is 3/6, which simplifies to 1/2.

To find the probability of both events happening, we multiply the individual probabilities:

Probability = (Probability of a multiple of three on the first die) * (Probability of an even number on the second die)
Probability = (1/3) * (1/2)
Probability = 1/6

Therefore, the probability that a multiple of three is rolled on one die and an even number is rolled on the second die is 1/6.