A single die is rolled 12 times. What is the probability that a six is rolled exactly once, if it is known that at least one six is rolled?

Question

I got 1-(5/6)^12 = 0.8878. But I am wrong in my answer. I am confused

Answer 1

A is the event exactly one 6

B is the event at least one 6

 

P(A) = 6*(1/6)(5/6)¹¹

P(B) = 1 - (5/6)¹²

 

P(A|B) = P(A ∩ B)/P(B) but P(A ∩ B) = P(A); therefore P(A|B) = (5/6)¹¹ / [1 - (5/6)¹²], approximately .15