Does any one knows answer for this question related to probability?
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 = ?
A. 2/3
B. 5/6
C. 1/6
D. 1/2
E. 1/3
The cases where the sum of the numbers is greater than 9 are:
64 65 66 55 56 and 46
of those 6 cases, how many contain a 6 ??
is that 5/6?
To find the probability that one of the numbers is a 6 given that the sum is greater than 9, we need to determine the total number of favorable outcomes and divide it by the total number of possible outcomes.
Let's first consider the favorable outcomes. For the sum to be greater than 9, the possible outcomes are (4,6), (5,6), and (6,6). Notice that in each of these cases, one of the numbers is a 6. So, we have a total of 3 favorable outcomes.
Now, let's determine the total number of possible outcomes when two fair dice are thrown. Each die has 6 possible outcomes (1, 2, 3, 4, 5, 6), and since we are throwing two dice, the total number of outcomes is 6 * 6 = 36.
So, the probability that one of the numbers is a 6 given that the sum is greater than 9 is 3/36.
However, we can simplify this fraction. Both 3 and 36 can be divided by 3, resulting in 1/12.
Now, we need to look at the answer choices given:
A. 2/3 - This is not equal to 1/12.
B. 5/6 - This is not equal to 1/12.
C. 1/6 - This is not equal to 1/12.
D. 1/2 - This is not equal to 1/12.
E. 1/3 - This is not equal to 1/12.
None of the answer choices match the calculated probability of 1/12, so none of the given options are the correct answer.