Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn at random. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?

$\frac{4}{7}$

The correct answer is Option (3) → $\frac{4}{7}$ ##

Let events

$A = \text{Number on the card drawn is even}$

$B = \text{Number on the card drawn is greater than 3}$

Sample space of the experiment is

$S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \quad [∴n(S) = 10]$

Then $A = \{2, 4, 6, 8, 10\}$, $B = \{4, 5, 6, 7, 8, 9, 10\}$

And $A \cap B = \{4, 6, 8, 10\}$

$∴$ $n(A) = 5, n(B) = 7 \text{ and } n(A \cap B) = 4$

Thus, $P(A) = \frac{5}{10}, P(B) = \frac{7}{10} \text{ and } P(A \cap B) = \frac{4}{10}$

Now,

$P(A | B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{4}{10}}{\frac{7}{10}} = \frac{4}{7}$