Probability with dice question

Question

Q: Find the probability of rolling 2 odd numbers or a sum of 10 when a pair of dice is rolled.

I have no idea how to solve/start this so any help is appreciated!

Answer 1

In order to solve this question, it is important to understand how joint probability (the likelihood of multiple events occurring simultaneously) is calculated. The equation is

P(A and B) = P(A)P(B)

Applying this to the first question above, A = rolling an odd number on Dice 1, B = rolling an odd number on Dice 2. On a dice, the probability of rolling an odd number is 3/6 = 1/2. So P(A) = P(B) = 1/2.

Using the equation above, P(A and B) = P(A)P(B) = 1/2 * 1/2 = 1/4.

For the second question, there are only three ways a sum of ten could be achieved by rolling two dice out of 36 (6 x 6) possible combination: 4, 6; 5, 5; 6, 4. Thus, the probability of this occurring is 3/36 = 1/12.