Question

You roll two dice. What is the probability that the sum of the dice is greater than 7 and one dice shows a 2? A 6x6 table of dice outcomes will help you to answer this question.
A. 2/15 B. 1/18 C. 1/36 D. 23/36

Answer 1

In this question, the condition asked is two which was
1. The dice sum >7 (notice that >7 mean at least 8)
2. One of the two dice show a 2

It will be easier to fulfill the No.2 condition first so you can divide the probability into two,
Case 1: 1st dice show 2: then the second dice need to be 6 to made it sum>7
Case 2:2nd dice show 2: then the second dice need to be 6 to made it sum>7

The probability for a dice showing 2 is 1/6. The probability for a dice showing 6 is 1/6. Then the probability is 1/6 * 1/6= 1/36 for each case
Since case 1 and case 2 has same probability, then you just need to multiply 1/36 *2 = 1/18