Two fair dice are thrown. If the first die thrown is a 3, what is the probability that the sum of the two dice is greater than 7?
Answer: 1/3. Thanks for any help
dice are numbered 1-6
How many of those numbers, when added to 3, make a sum greater than 7?
To find the probability that the sum of the two dice is greater than 7 given that the first die thrown is a 3, we can use conditional probability.
First, let's determine the total number of outcomes when throwing two dice. Each die has 6 possible outcomes, so the total number of outcomes is 6 × 6 = 36.
Next, we need to find out how many outcomes result in the first die being a 3. Since there are 6 possible outcomes for the second die when the first die is a 3, there are a total of 6 outcomes where the first die is a 3.
Now, we need to count how many of these outcomes have a sum greater than 7. When the first die is a 3, there are 4 possible outcomes for the second die that would result in a sum greater than 7: (3, 5), (3, 6), (4, 4), and (4, 5).
Therefore, the probability that the sum of the two dice is greater than 7 given that the first die thrown is a 3 is 4/6.
Simplifying, the probability is 2/3.
So, the correct answer is 2/3, not 1/3.