Answer:
Explanation:
To find the probability of the sum of two randomly selected numbers from a set being greater than 12, we need to first find the total number of possible combinations of two numbers and then count the number of combinations that result in a sum greater than 12.
The set contains four numbers, so there are 4 choose 2 possible combinations of two numbers, which is equal to (4! / (2! * (4 - 2)!)), or 6 combinations. These combinations are:
(0,6), (0,12), (0,15), (6,12), (6,15), (12,15)
Next, we'll count the number of combinations that result in a sum greater than 12. These combinations are:
(6,15), (12,15)
There are 2 combinations that result in a sum greater than 12.
Finally, to find the probability, we'll divide the number of favorable outcomes (combinations with a sum greater than 12) by the total number of outcomes (all possible combinations of two numbers), and express the result as a fraction:
probability = 2 / 6
Reducing the fraction, we get:
probability = 1 / 3
So, the probability that the sum of two randomly selected numbers from the set is greater than 12 is 1/3.
That's how you find the probability of the sum of two randomly selected numbers from a set being greater than a certain value. By counting the number of favorable outcomes and dividing by the total number of possible outcomes, you can find the probability of a certain event.