Question

Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. 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?

Answer 1

Sample space, S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Consider the given events.
A = An even number on the card
B = A number more than 3 on the card

Clearly,
A = {2, 4, 6, 8, 10}
B = {4, 5, 6, 7, 8, 9, 10}

\[\text{ Now } , \]
\[A \cap B = \left\{ 4, 6, 8, 10 \right\}\]
\[ \therefore \text{ Required probability } = P\left( A/B \right) = \frac{n\left( A \cap B \right)}{n\left( B \right)} = \frac{4}{7}\]