Question

Let A be the event that either a 3 or 4 is rolled first, followed by an even number. Let B be the event that the sum of the two rolls is at most 7. Find P(A|B)

Answer 1

To find P(A|B), first calculate P(A) and P(B). Then use the formula P(A|B) = P(A ∩ B) / P(B). P(A|B) = 1/21.

Step-by-step explanation:

To find P(A|B), we first need to find P(A) and P(B). Let's start with P(A). The event A consists of rolling either a 3 or 4 first, followed by an even number. There are 6 possible outcomes for the first roll and 6 possible outcomes for the second roll. Out of these 36 outcomes, there are 4 outcomes where either a 3 or 4 is rolled first, followed by an even number. Therefore, P(A) = 4/36 = 1/9.

Next, let's find P(B). The event B consists of the sum of the two rolls being at most 7. To calculate this probability, we can list out all the possible outcomes that satisfy this condition. There are 21 outcomes where the sum is at most 7 out of a total of 36 possible outcomes. Therefore, P(B) = 21/36 = 7/12.

Finally, we can use the formula P(A|B) = P(A ∩ B) / P(B) to find P(A|B). The intersection of A and B consists of the outcomes where either a 3 or 4 is rolled first, followed by an even number and the sum of the two rolls is at most 7. There is only 1 outcome that satisfies this condition, which is rolling a 3 first and then rolling a 2. Therefore, P(A|B) = 1/36 = 1/21.