Answer:
Explanation:
To find the probability that the sum of the outcomes is 10 or greater when a 5 appears on the first die, we need to consider all possible outcomes when a 5 appears on the first die and then calculate how many of those outcomes result in a sum of 10 or greater.
When a 5 appears on the first die, the second die can show any number from 1 to 6. We'll list all the possible outcomes where a 5 appears on the first die:
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
Now, let's calculate the sums for these outcomes:
5 + 1 = 6
5 + 2 = 7
5 + 3 = 8
5 + 4 = 9
5 + 5 = 10
5 + 6 = 11
Out of these outcomes, the sums that are 10 or greater are 10, 11. So, there are 2 outcomes that meet the condition.
Now, let's calculate the total number of possible outcomes when two dice are thrown. Each die has 6 sides, so there are 6 * 6 = 36 possible outcomes when two dice are thrown.
Now, we can calculate the probability:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
Probability = 2 / 36
You can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:
Probability = (2 ÷ 2) / (36 ÷ 2)
Probability = 1/18
So, the probability that the sum of the outcomes is 10 or greater when a 5 appears on the first die is 1/18.