Two numbers rolled can be added to get a sum. Find P(sum is even.)
1/4
15/36
1/2
3/4
geee,
of the 36 sums possible, half would be even and half would be odd
so Prob(even) = 1/2
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!
To find the probability of the sum being even when two numbers are rolled, we need to determine the number of favorable outcomes (rolling even sums) divided by the total number of possible outcomes.
First, let's list all the possible outcomes when rolling two dice. Each dice has six sides numbered 1 to 6, so the total number of possible outcomes is 6 * 6 = 36.
To find the favorable outcomes (even sums), we can list them as follows:
1 + 1 = 2
1 + 3 = 4
1 + 5 = 6
2 + 2 = 4
2 + 4 = 6
2 + 6 = 8
3 + 1 = 4
3 + 3 = 6
3 + 5 = 8
4 + 2 = 6
4 + 4 = 8
4 + 6 = 10
5 + 1 = 6
5 + 3 = 8
5 + 5 = 10
6 + 2 = 8
6 + 4 = 10
6 + 6 = 12
Now we count the number of even sums, which is 9.
Therefore, the probability of rolling an even sum is P(sum is even) = favorable outcomes / total outcomes = 9 / 36 = 1/4.
So, the correct option is 1/4.
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.