12 cards numbered 1 to 12 are placed in a box, mixed up thoroughly, and then a card is drawn at random from the box. If it is known that the number on the drawn card is more than 4, find the probability that it is an even number.

1/2

E = Number on the card drawn is even

F = Number on the card drawn is more  than 4

E \(=\begin{Bmatrix}2 & 4 & 6 & 8 & 10 & 12\end{Bmatrix}\)

F \(= \begin{Bmatrix}5 & 6 & 7 & 8 & 9 & 10 & 11 & 12\end{Bmatrix}\)

\(E\cap F = \begin{Bmatrix}6 & 8 & 10 & 12\end{Bmatrix}\)

\(P(E) = \frac{6}{12} = \frac{1}{2}\),

\(P(F) = \frac{8}{12} = \frac{8}{3}\)

\(P(E\cap F) = \frac{4}{12} = \frac{1}{3}\)

\(P(E/F) = \frac{P(E\cap F)}{P(F)}\)

\(P(E/F) = \frac{1/3}{2/3} = \frac{1}{2}\)