If two fair dice are rolled, find the probability of a sum of 6 given that the roll is a "double".
How do I do this?
let A be "sum of 6" and B be "double"
What you have is P(A│B) , read as
the probability of A given B
which is defined as P(A AND B)/P(B)
Prob(A AND B) = Prob(sum of 6 AND a double) = 1/36
Prob(B) = 6/36 = 1/6
so Prob(sum of 6 AND a double) = (1/36)÷(1/6)
= (1/36)(6/1) = 1/6
Well, it's all about probability, my friend! Let's break it down step by step.
First, we need to find the probability of rolling a double. Since there are six possible outcomes on a single fair die (the numbers 1 to 6), and there are two dice being rolled, the total number of possible outcomes when rolling two fair dice is 6 * 6 = 36.
Out of those 36 possible outcomes, there are six outcomes that result in a double (1-1, 2-2, 3-3, 4-4, 5-5, 6-6).
So, the probability of rolling a double is 6/36, which simplifies to 1/6.
Now, we want to find the probability of getting a sum of 6 given that we roll a double. Since we know we rolled a double, we only need to consider the outcomes where both dice showing the same number.
Out of the six possible doubles, only one of them results in a sum of 6, which is the combination of two 3's.
Therefore, the probability of rolling a sum of 6 given that we rolled a double is 1/6.
So, the answer to your question is 1/6.
Hope that puts a smile on your face!
To find the probability of a sum of 6 given that the roll is a "double" when two fair dice are rolled, you can follow these steps:
Step 1: Determine the total number of outcomes when rolling two dice. Each die has 6 possible outcomes, so the total number of outcomes is 6 * 6 = 36.
Step 2: Calculate the total number of outcomes where the roll is a "double". A "double" means that both dice show the same number when rolled. There are 6 possible doubles: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6).
Step 3: Calculate the number of outcomes where the sum is 6 given that the roll is a "double". In this case, the only possible outcome is (3, 3), since it is the only double that adds up to 6.
Step 4: Calculate the probability by dividing the number of favorable outcomes (only 1 in this case) by the total number of possible outcomes (36).
Probability = Number of favorable outcomes / Total number of possible outcomes = 1 / 36
Therefore, the probability of obtaining a sum of 6 given that the roll is a "double" is 1/36.
To find the probability of a sum of 6 given that the roll is a "double", we first need to determine the probability of getting a double.
Since there are 6 possible outcomes for each dice roll (1, 2, 3, 4, 5, 6), the total number of possible outcomes when rolling two dice is 6 x 6 = 36.
Next, we need to find the number of ways to get a double.
There are 6 possible doubles: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6).
So the probability of getting a double is 6/36, which can be simplified to 1/6.
Now, given that the roll is a double, we need to find the probability of the sum being 6.
Out of the 6 possible doubles, only two of them add up to a sum of 6: (1, 5) and (5, 1).
Therefore, the probability of a sum of 6 given that the roll is a double is 2/6, which simplifies to 1/3.