Question

Two dice are thrown. If each face is equally likely to turn up, find the probability that the sum is at least 7. (Write your answer as a fraction.)

Answer 1

Let's count. Look at the chart showing the sample space for tossing a pair of dice. You want a sum of at least 7. The sums of 7 are ringed in red.

Follow the sums down the right to left diagonals.
6 ways to get a sum of 7
5 ways to get a sum of 8
4 ways to get a sum of 9
3 ways to get a sum of 10
2 ways to get a sume of 11
1 way to get a sum of 12.

Notice the cool pattern.

21 ways to get a sum greater than or equal to 7.

Answer 2

P(at least a sum of 7) = 21/ 36. That simplifies to 7/12.

36 is the number of outcomes of tossing a pair of dice: 6 ways for the first and 6 for the second = 36.

Answer 3

i swear i just answered this one...