Multiple choice

I have $3$ normal disc, one red, one blue and one green and I roll all three simultaneously. Let $P$ be the porbability that the sum of the numbers on the red and blue dice is equal to the number on the green die. If $P$ is the written in lowest terms as $a/b$ then the value of $(a+b)$ equals-

  1. $79$
  2. $77$
  3. $61$
  4. $57$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are 216 equally likely outcomes when three dice are rolled. Favorable outcomes satisfy red + blue = green, and the possible sums from 2 through 6 contribute 1 + 2 + 3 + 4 + 5 = 15 outcomes, so P = 15/216 = 5/72 and a + b = 77.

AI explanation

The total number of outcomes when rolling three dice is 6 times 6 times 6, which is 216. We must find combinations where the sum of the red and blue dice equals the green die, such as (1,1,2) and (2,2,4); counting all such valid arrangements across the three dice yields exactly 15 favorable outcomes. The probability is 15/216, which simplifies to 5/72. Adding the numerator 5 and the denominator 72 gives the result 77.

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