Question

Assertion (A): A card is drawn at random from a well-shuffled pack of 52 cards. The probability that the card drawn is not an ace is \[\frac{9}{13}\].

Reason (R): When randomly drawing out a card from a well-shuffled pack of cards, the event of drawing out an ace card and the event of drawing out a non-ace card are complementary events.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is false and Reason (R) is true.

Explanation:

Step 1 – Assertion: A is false. There are 48 non-ace cards in the pack, so the probability is \[\frac{48}{52}=\frac{12}{13},\] not \[\frac{9}{13}.\]

Step 2 – Reason: R is true. Drawing an ace and drawing a non-ace are complementary events.