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mathmath333

  • one year ago

Probability question

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align}& \normalsize \text{Find the probability that when a hand of 7 cards is drawn from a well}\hspace{.33em}\\~\\ & \normalsize \text{shuffled deck of 52 cards, it contains atleast 3 Kings.}\hspace{.33em}\\~\\ \end{align}}\)

  2. mathmath333
    • one year ago
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    Total number of possible hands = 52C7

  3. ganeshie8
    • one year ago
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    How many kings are there in a full deck ?

  4. mathmath333
    • one year ago
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    4

  5. phi
    • one year ago
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    break the "good" hands into the problem of choosing 4 "not kings" and 3 kings plus prob of choosing 3 not kings, and 4 kings

  6. mathmath333
    • one year ago
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    what u mean ?

  7. phi
    • one year ago
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    how many ways can you choose 4 "not kings" from the deck?

  8. mathmath333
    • one year ago
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    48

  9. phi
    • one year ago
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    48C4

  10. mathmath333
    • one year ago
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    yes

  11. phi
    • one year ago
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    that gives you all the "4 card" hands with no kings now pick 3 kings from the king pile (4 cards) 4C3 multiply to get the number of hands with exactly 3 kings

  12. phi
    • one year ago
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    next, we want the number of hands with 4 kings

  13. mathmath333
    • one year ago
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    4C3\(\times \)48C4

  14. mathmath333
    • one year ago
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    4C4×48C3

  15. phi
    • one year ago
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    ok, now add that is the numerator (# of hands that match our criteria) as you know the denominator is 52C7

  16. mathmath333
    • one year ago
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    =\(\dfrac{4C4×48C3+4C3×48C4}{52C7}\)

  17. phi
    • one year ago
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    yes

  18. mathmath333
    • one year ago
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    thnks

  19. phi
    • one year ago
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    yw

  20. Loser66
    • one year ago
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    Thank you very much @phi . I am always in trouble with probability. Your method is PERFECT. It is easy to understand what is going on. Thanks you so much.

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