A pair of fair dice is tossed once. If the sum of the two numbers is greater than 9, the probability that one of the numbers is a 6 =
Knowing that the sum is greater than 9, there are only 4 possibilities:
46
55
56
66
Looks like p=3/4
Rolling two standard 6-sided dice, there is 1 way to get a sum of 12, 2 ways to get a sum of 11, and 3 ways to get a sum of 10. That’s 6 out 36 possible outcomes for a probability of 1/6.
To find the probability that one of the numbers is a 6 given that the sum is greater than 9, we need to first determine the total number of outcomes that satisfy both conditions.
Step 1: Determine the total number of outcomes when two fair dice are tossed.
Each die has 6 sides, so the total number of outcomes when two dice are tossed is 6 * 6 = 36.
Step 2: Determine the number of outcomes where the sum is greater than 9.
We can find these outcomes by listing all the possible combinations where the sum is greater than 9: (4, 6), (5, 5), (5, 6), (6, 4), (6, 5), and (6, 6).
Thus, there are 6 outcomes where the sum is greater than 9.
Step 3: Determine the number of outcomes where one of the numbers is a 6.
From the list of outcomes above, we can see that in the combinations (4, 6), (5, 6), (6, 4), (6, 5), and (6, 6), one of the numbers is a 6. So, there are 5 outcomes where one of the numbers is a 6.
Step 4: Calculate the probability.
To calculate the probability, we divide the number of favorable outcomes (5) by the total number of outcomes (36):
Probability = Number of favorable outcomes / Total number of outcomes
= 5 / 36 = 5/36
Therefore, the probability that one of the numbers is a 6 given that the sum is greater than 9 is 5/36.