The probability that Katarina will correctly solve a given Brilliant math problem is 1/8. The probability that Layla will solve the same problem correctly is 1/12. The probability that they will give the same incorrect numerical result is 1/1001. Suppose Katarina and Layla solve a Brilliant math problem independently and get the same result. The probability that they get the correct answer, given that they got the same result, can be written as a/b, where a and b are coprime positive integers. Find a+b.

97 go solve it yourself.

97 is incorrect...

To find the probability that Katarina and Layla both get the correct answer given that they got the same result, we can use Bayes' theorem.

Let's define the following events:
A = Katarina gets the correct answer
B = Layla gets the correct answer
C = Katarina and Layla get the same result

We want to find P(A|C), the probability of event A given that event C occurred.

Bayes' theorem states:
P(A|C) = (P(C|A) * P(A)) / P(C)

We are given:
P(A) = 1/8 (probability that Katarina gets the correct answer)
P(B) = 1/12 (probability that Layla gets the correct answer)
P(C) = ? (probability that Katarina and Layla get the same result)

To find P(C), let's consider the two cases where:
- Katarina and Layla both get the answer correct
- Katarina and Layla both get the answer incorrect

Case 1: Both get the correct answer
The probability that both Katarina and Layla simultaneously get correct answers is:
P(A ∩ B) = P(A) * P(B) = (1/8) * (1/12) = 1/96

Case 2: Both get the incorrect answer
The probability that both Katarina and Layla simultaneously get incorrect answers is:
P(A' ∩ B') = (1 - P(A)) * (1 - P(B)) = (7/8) * (11/12) = 77/96

Based on the given information, we are also told that the probability that they give the same incorrect numerical result is 1/1001. This can be interpreted as the probability of the intersection of the complement events A' and B' (i.e., P(A' ∩ B')). So we have:
P(A' ∩ B') = 1/1001 = 77/96
Solving for P(C) (the probability that Katarina and Layla get the same result):
P(C) = P(A ∩ B) + P(A' ∩ B') = 1/96 + 77/96 = 78/96 = 13/16

Now, we can substitute the values into Bayes' theorem to find P(A|C):
P(A|C) = (P(C|A) * P(A)) / P(C)
P(A|C) = (1 * 1/8) / (13/16)
P(A|C) = 16/104
P(A|C) = 2/13

Therefore, a = 2 and b = 13. So, a + b = 2 + 13 = 15.

Therefore, the answer is 15.