Two dice are rolled. Determine the probability of the following. rolling an even sum and a sum greater than

Answer 1

If by this you mean that the sum is both even and greater than 6, then a roll of 8, 10, or 12 satisfies the condition.

There are 5 ways to get an 8. A three on one die and a five on the other die, a 2 on one die and a 6 on the other die, or a four on each die.

There are three ways to get a 10. A 6 on one die and a 4 on the other die, or a 5 on each die.

There is one way to get a 12, a six on each die.

So adding these up there are 9 ways to get an even number greater than 6.

There are 36 total outcomes for rolling the dice (6 possibilities for each die), so the probabilkity of rolling an even number greater than 6 is 9/36 = 1/4

If, however, these are separate events, then there are two separate probabilities to be calculated.

First, the probability of rolling an even number:

You can either have an odd number on each die, or an even number on each die. There is a 1/2 probability of rolling either an odd or even number, so both probabilities are 1/2 x 1/2 + 1/4, and adding those together gives a 1/2 probability of rolling any even number.

There are 5 ways to roll a total of 6, a 1 and a 5 on either die, a 2 or a 4 on either die, or a three on both. So the probability of rolling a 6 is 5/36.

Hope this helps.