Question

What is the probability that the sum of the dice is odd and 1 die shows a 5?

Answer 1

How many dice are being rolled?

Answer 2

If the number of dice is = 2 then:

The chance of 1 of the dice landing on 5 is:

\[P = \frac{A}{N}\]

P = Probability of a 5
A = Amount of 5s in the roll = 2
N = Number of total sides = 12

\[P = \frac{2}{12} or \frac{1}{6}\]

Then we calculate the chance of the two dices' sum being odd.

5 + 1 = 6 X
5 + 2 = 7 √
5 + 3 = 8 X
5 + 4 = 9 √
5 + 5 = 10 X
5 + 6 = 11 √

So the probability of landing a number that will add with 5 and result in an odd value is 3 out of 6, or, 1 out of 2.

So we have a 1 out of 6 chance of rolling a 5, and a 1 out of 2 chance of rolling a number that will give you an odd sum. When dealing with compounding probability you multiply the probabilities of each part of the scenario together to get the probability of both occurring in the same instance.

\[\frac{ 1 }{ 6 } * \frac{ 1 }{ 2 } = \frac{1}{12}\]

So there is a 1 out of 12 chance of rolling a 5 and rolling a number that will sum out to an odd number in the same roll.

I really hope it was only 2 dice, if I was wrong tell me and i'll work it all out for you and show you that probability as well.