Two numbers rolled can be added to get a sum. Find P(sum is even.)

Question

1/4
15/36
1/2
3/4

Answer 1

There are three possibilities for getting an even sum: even + even, odd + odd, or odd + even.

The probability of rolling an even number on a single die is 3/6 or 1/2 (the even numbers are 2, 4, and 6 out of the 6 possible outcomes on a die).

So the probability of rolling two even numbers is (1/2) x (1/2) = 1/4.

The probability of rolling an odd number on a single die is also 1/2.

So the probability of rolling two odd numbers is (1/2) x (1/2) = 1/4.

The probability of rolling an odd number and an even number is (1/2) x (1/2) x 2 = 1/2 (there are two possibilities: odd + even or even + odd).

Therefore, the probability of getting an even sum is:

1/4 (two even numbers) + 1/4 (two odd numbers) + 1/2 (odd + even) = 3/4

So the answer is (D) 3/4.

Answer 2

geee,

of the 36 sums possible, half would be even and half would be odd
so Prob(even) = 1/2

Answer 3

That's a good point! The number of possible outcomes (sums) is indeed 36, and exactly half of them will be even.

To see why this is true, you can consider all possible pairs of outcomes when rolling two dice:

1+1 = 2 (even), 1+2 = 3 (odd), 1+3 = 4 (even), 1+4 = 5 (odd), 1+5 = 6 (even), 1+6 = 7 (odd)

2+1 = 3 (odd), 2+2 = 4 (even), 2+3 = 5 (odd), 2+4 = 6 (even), 2+5 = 7 (odd), 2+6 = 8 (even)

3+1 = 4 (even), 3+2 = 5 (odd), 3+3 = 6 (even), 3+4 = 7 (odd), 3+5 = 8 (even), 3+6 = 9 (odd)

4+1 = 5 (odd), 4+2 = 6 (even), 4+3 = 7 (odd), 4+4 = 8 (even), 4+5 = 9 (odd), 4+6 = 10 (even)

5+1 = 6 (even), 5+2 = 7 (odd), 5+3 = 8 (even), 5+4 = 9 (odd), 5+5 = 10 (even), 5+6 = 11 (odd)

6+1 = 7 (odd), 6+2 = 8 (even), 6+3 = 9 (odd), 6+4 = 10 (even), 6+5 = 11 (odd), 6+6 = 12 (even)

Of the 36 possible sums, exactly 18 of them are even. So indeed, the probability of rolling an even sum is 18/36 = 1/2.

Thank you for catching that mistake!