Assertion (A) : The probability of drawing a red face card, at random, from a well-shuffled pack of 52 playing cards is $\frac{3}{26}$. Reason (R) : The number of face cards in a pack of 52 playing cards is 16.

Step 1: Analyze the Assertion (A)

To verify the assertion, we need to calculate the probability of drawing a red face card from a standard deck of 52 playing cards. This involves identifying the number of favorable outcomes (red face cards) and the total number of possible outcomes (total cards).

Step 2: Calculate Number of Red Face Cards

A standard deck has 4 suits: hearts, diamonds, clubs, and spades. Hearts and diamonds are red suits. Each suit has 3 face cards: King, Queen, and Jack. Therefore, the number of red face cards is $3 \text{ (from hearts)} + 3 \text{ (from diamonds)} = 6$.

Step 3: Calculate the Probability

Now we can calculate the probability. The number of red face cards is 6, and the total number of cards is 52. So, the probability is $\frac{6}{52}$, which simplifies to $\frac{3}{26}$. This matches the assertion.

Step 4: Analyze the Reason (R)

The reason states that the number of face cards in a pack of 52 playing cards is 16. A standard deck has 4 suits (hearts, diamonds, clubs, spades), and each suit has 3 face cards (King, Queen, Jack). Therefore, the total number of face cards is $3 \times 4 = 12$. This contradicts the reason.

Step 5: Conclusion

Based on our calculations, the Assertion (A) is true because the probability of drawing a red face card is indeed $\frac{3}{26}$. However, the Reason (R) is false because there are 12 face cards in a deck, not 16.

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