two numbers rolled can be added to get a sum. Find P(sum is even) is it 1/4 ?
How did you get that answer?
To find the probability that the sum of two rolled numbers is even, we need to understand two things:
1. The possible outcomes when rolling two numbers.
2. The number of outcomes that result in an even sum.
1. Possible outcomes when rolling two numbers:
When rolling two dice, each die can have 6 possible outcomes (numbers 1-6). So, the total number of possible outcomes when rolling two dice is 6 * 6 = 36.
2. Outcomes resulting in an even sum:
To find the number of outcomes that result in an even sum, we need to consider the possible combinations of numbers rolled. Here are the possible combinations and their sums:
- 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)
From the list above, we can see that there are 18 outcomes that result in an even sum.
Now, to find the probability, we divide the number of outcomes that result in an even sum by the total number of possible outcomes:
P(sum is even) = Number of outcomes resulting in an even sum / Total number of possible outcomes = 18 / 36 = 1/2.
Therefore, the correct probability is 1/2, not 1/4.