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anonymous

  • one year ago

MEDAL!! (refer to choosing two cards from a thoroughly shuffled deck. Assume that the deck is shuffled after a card is returned to the deck) If you put the first card back in the deck before you draw the next, what is the probability that the first card is a 10 and the second card is a jack?

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  1. jim_thompson5910
    • one year ago
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    Focus on one card at a time. What is the probability of pulling out a "10" card ?

  2. jim_thompson5910
    • one year ago
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    here's a visual of all the cards (52 total; 4 suits, 13 per suit) http://www.jfitz.com/cards/classic-playing-cards.png

  3. anonymous
    • one year ago
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    hmm, there are four 10s

  4. jim_thompson5910
    • one year ago
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    yes, so the probability of picking a single 10 is?

  5. anonymous
    • one year ago
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    guessing 4 out of 52

  6. jim_thompson5910
    • one year ago
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    you can reduce that fraction to get ?

  7. jim_thompson5910
    • one year ago
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    4/52 = ???

  8. anonymous
    • one year ago
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    1/13

  9. jim_thompson5910
    • one year ago
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    yes

  10. jim_thompson5910
    • one year ago
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    so if you focus on one suit only, there is a 1 in 13 chance to get a "10" card

  11. jim_thompson5910
    • one year ago
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    next step: find the probability of picking a jack. All 52 cards are still there since the first card was put back (it says `Assume that the deck is shuffled after a card is returned to the deck`)

  12. anonymous
    • one year ago
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    if there are 4 jacks wouldn't it be 4/52=1/13 again?

  13. jim_thompson5910
    • one year ago
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    yep

  14. jim_thompson5910
    • one year ago
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    now multiply the two fractions

  15. jim_thompson5910
    • one year ago
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    P(10 on first draw, jack on second draw) = P(10 on first draw) * P(jack on second draw) this works because the two events are independent

  16. anonymous
    • one year ago
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    multiplying the two fractions would get me 1/169

  17. jim_thompson5910
    • one year ago
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    which is the correct final answer

  18. anonymous
    • one year ago
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    thanks again jim!

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