if you have two fair dice that are rolled, what is the probability of a sum 6 given that the roll is a 'double'?
Given that the roll is a double, there are only 6 possibilities - because each number is rolled twice:
1-6, rolled twice.
So there are a total of 6 possibilities.
How many of those have a sum of 6?
Probability = n/total
thanks!!
5/36
To calculate the probability of a sum of 6 given that the roll is a 'double', we first need to determine the probability of rolling a double with two fair dice.
A double can only occur when both dice show the same number. There are 6 possible outcomes for each dice (numbers 1 to 6), so there are 6 possible doubles: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).
Since each die has 6 equally likely outcomes, the total number of possible outcomes for rolling two dice is 6 * 6 = 36.
The probability of rolling a double is therefore 6/36, which simplifies to 1/6.
Now, given that we rolled a double, we want to find the probability of getting a sum of 6.
Out of the six possible doubles we listed earlier, only one has a sum of 6: (3,3).
Therefore, the probability of getting a sum of 6 given that the roll is a double is 1 out of 6 possible outcomes, or 1/6.