Probability - A and B are two weak students

[zorro]

Probability - A and B are two weak students....

Homework Statement

A and b are two weak students in Mathematics. The chances of their solving a problem correctly is 1/8 and 1/12. The probability of them making a common mistake is 1/1001 and they obtain the same answer. Find the chance that their answer is correct.

The Attempt at a Solution

Let E1 be the event that A and B solve correctly
E2 be the event that A and B solve incorrectly.
K be the event that they obtain same answer.

P(E1) = 1/8 x 1/12
P(K/E1)= 1000/1001
P(E2) = 7/8 x 11/12
P(K/E2) = 1/1001

Now by Baye's theorem,

P(E1/K) = P(E1)xP(K/E1)/.........

I got the answer as 1000/1077
The answer given is

Spoiler

13/14

There is a very very small difference in two answers.They are correct upto 3 decimal places.

Please tell me where is my mistake.

 

[verty]

If I understand correctly, P(K/E1) = 1. If they both get the correct answer, they get the same correct answer.

 

[zorro]

You are right. I got it.
Thank you verymuch!