Assertion (A) : The probability of drawing a red face card, at random, from a well-shuffled pack of 52 playing cards is 263.
Reason (R) : The number of face cards in a pack of 52 playing cards is 16.
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Step-by-Step Solution
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 (from hearts)+3 (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 526, which simplifies to 263. 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 3×4=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 263. However, the Reason (R) is false because there are 12 face cards in a deck, not 16.