Two dice are rolled and the sum of the outcomes is counted.
Find the probability that the sum is smaller than 4.
only 3 of the 36 possible throws sum to less than 4. So, ...
the only cases out of 36 would be
11,12, 21
so 3/36 or 1/6
arghhh
of course lately
3/36 = 1/12 ,not 1/6
To find the probability that the sum of the outcomes is smaller than 4 when two dice are rolled, we need to determine the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the number of favorable outcomes, which are the outcomes that satisfy the condition of having a sum smaller than 4.
To have a sum smaller than 4, we can only get a sum of 2 or 3, since those are the only possible outcomes that satisfy the condition.
For a sum of 2, there is only one possible outcome: rolling a 1 on both dice.
For a sum of 3, there are two possible outcomes: rolling a 1 and a 2, or rolling a 2 and a 1.
So, the number of favorable outcomes is 1 (for a sum of 2) + 2 (for a sum of 3) = 3.
Now, let's determine the total number of possible outcomes when two dice are rolled. Each die has 6 sides, and there are two dice, so the total number of outcomes is 6 * 6 = 36.
Therefore, the probability that the sum is smaller than 4 is 3 favorable outcomes divided by 36 total outcomes:
Probability = Favorable outcomes / Total outcomes
= 3 / 36
= 1 / 12
So, the probability that the sum is smaller than 4 when two dice are rolled is 1/12.