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GOODMAN

Two cards are drawn from a standard deck of 52 cards without replacement. What is the probability that both cards are greater than 2 and less than 9?

  • one year ago
  • one year ago

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  1. ParthKohli
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    Okay, I'll help you with this :)

    • one year ago
  2. GOODMAN
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    Thanks little bro, lol. I am studying and forgot this all.

    • one year ago
  3. ParthKohli
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    What would be the probability of getting a card between 2 and 9 in the first pick?

    • one year ago
  4. GOODMAN
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    2/52 and 9/52

    • one year ago
  5. ParthKohli
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    No...it's saying that it's greater than 2 and less than 9. 3,4,5,6,7,8 are the numbers that qualify for me :)

    • one year ago
  6. GOODMAN
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    So we have to get the ones in between?

    • one year ago
  7. ParthKohli
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    Yes.. exactly

    • one year ago
  8. ParthKohli
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    Since there are 3,4,5,6,7,8 in four suits, the probability would be: \( \color{Black}{\Rightarrow \Large {4 \times 6 \over 52} }\) For the first pick.

    • one year ago
  9. ParthKohli
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    Simplifying further: \( \color{Black}{\Rightarrow \Large {24 \over 52} = {12 \over 26} = {6 \over 13} }\)

    • one year ago
  10. ParthKohli
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    Now we've picked the first. We have 1 card LESS in the deck because we haven't replaced the cards.

    • one year ago
  11. ParthKohli
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    So this time the denominator of the probability would become 51. The numerator will also get one less because we have assumed that we have picked one card which is 3,4,5,6,7 or 8.

    • one year ago
  12. ParthKohli
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    There are 23 cards left that we want. 51 total cards left. \( \color{Black}{\Rightarrow \Large {23 \over 51} }\)

    • one year ago
  13. GOODMAN
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    Okay...so since we had not replaced, we have to subtract 1?

    • one year ago
  14. ParthKohli
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    Now if we want two things to happen at the same time, we shall multiply the probabilities. \( \color{Black}{\Rightarrow \Large {13 \over 26} \times {23 \over 51}}\)

    • one year ago
  15. ParthKohli
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    We have to subtract 1 from both numerator and denominator.

    • one year ago
  16. GOODMAN
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    Thats it?

    • one year ago
  17. ParthKohli
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    Nope

    • one year ago
  18. GOODMAN
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    Wait. so after we multiply, we have to simplify further too?

    • one year ago
  19. ParthKohli
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    Oops.. I meant this: \( \color{Black}{\Rightarrow \Large {6 \over 13} \times {23 \over 51}}\)

    • one year ago
  20. ParthKohli
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    Multiply the fractions. The fractions are in their simplest forms so when we'll multiply it'd be in the simplest form.

    • one year ago
  21. GOODMAN
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    Yes, i did that. Okay, so 46/221 is final answer?

    • one year ago
  22. ParthKohli
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    How did you get that?

    • one year ago
  23. ParthKohli
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    Oh yes

    • one year ago
  24. ParthKohli
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    \( \color{Black}{\Rightarrow \Large {2 \over 13} \times {23 \over 17} }\)

    • one year ago
  25. ParthKohli
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    Correct! :D

    • one year ago
  26. GOODMAN
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    Okay, thats awesome!! Thanks soo much Parth!! Probability is my weak spot :/

    • one year ago
  27. ParthKohli
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    Haha probability is easy...getting the hang of what it involves is important

    • one year ago
  28. GOODMAN
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    Yea, see, im reviewing this since last semester, lol.

    • one year ago
  29. ParthKohli
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    And I've helped someone on this site after a long time. we usually just answer questions ://

    • one year ago
  30. GOODMAN
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    Thanks, I actually learned :D

    • one year ago
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