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From a pack of regular from a playing cards, two cards are drawn at random. What is the probability that both cards will be Kings, if first card in NOT replaced 
  • a)
    1/26
  • b)
    1/52
  • c)
    1/169
  • d)
    1/221
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
From a pack of regular from a playing cards, two cards are drawn at ra...
Here sample space S = 52
∴The probability  of drawing both cards are king without replacement  
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Most Upvoted Answer
From a pack of regular from a playing cards, two cards are drawn at ra...
Understanding the Problem
To find the probability of drawing two Kings from a standard deck of playing cards without replacement, we first recognize that a standard deck contains 52 cards, including 4 Kings.
Calculating the Probability
1. First Card Draw
- When the first card is drawn, there are 4 Kings out of 52 total cards.
- The probability of drawing a King first:
- P(King 1) = 4/52
2. Second Card Draw
- After drawing the first King, 51 cards remain in the deck, including 3 Kings.
- The probability of drawing a second King:
- P(King 2 | King 1 drawn) = 3/51
3. Combined Probability
- To find the probability of both events happening (drawing two Kings), we multiply the probabilities of each event:
- P(Both Kings) = P(King 1) * P(King 2 | King 1 drawn)
- P(Both Kings) = (4/52) * (3/51)
Calculating the Final Probability
- P(Both Kings) = (4/52) * (3/51)
- Simplifying:
- = (4 * 3) / (52 * 51)
- = 12 / 2652
- = 1 / 221
Conclusion
The probability that both cards drawn are Kings, given that the first card is not replaced, is indeed 1/221. Hence, the correct answer is option D.
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