Two fair dice are rolled. What is the conditional probability that at least one lands on 6 given that the dice land on different numbers? $F =$ The probability that the dice land on different numbers
$F = {(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)}$
$F = \frac{30}{36} = \frac{5}{6}$
$E =$ The event that at least one lands on 6
$E = {(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}$
$E = \frac{11}{36}$
What is the probability of E, when given that F has occurred?
$P = \frac{P(EF)}{P(F)}$
$P = \frac{1-P(EF^c)}{P(F)}$
$P =  \frac{\frac{11}{36}}{\frac{5}{6}}$
$P = \frac{11}{30}$
This answer was incorrect it is $\frac{1}{3}$ I think there is an issue in identifying $P(EF)$, what should that be and why? Identifying F is easy because that is what is given to have occurred.
Added: Is $EF$ equivalent to $E \cap F$?

You have made a mistake. In event E, $(6,6)$ is not an option, since it is given that dices are to land on different numbers. So you have only 10 such. So the probability is, going by your method, ${10\over{36}}\over{5\over6}$
This is $1\over3$.
