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anonymous

  • one year ago

A box contains 12 plastic forks and 6 plastic knives. If two utensils are chosen at random from the box without replacement, what is the probability that they are different? A) 13 17 B) 4 17 C) 8 17 D) 9 17 PLEASEE EXPLAIN HOW TO DO THIS. I don't just want the answer :) Thank you VERY much.

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  1. anonymous
    • one year ago
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    So there are 18 total utensils in the box. What's the probability that a fork is drawn first?

  2. anonymous
    • one year ago
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    12 over 18?

  3. anonymous
    • one year ago
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    Correct. It can be reduced to 2/3. The fork is NOT replaced so there are now 17 utensils in the box. What's the probability that a knife is chosen next?

  4. anonymous
    • one year ago
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    6 over 17

  5. anonymous
    • one year ago
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    Very good. So the probability that a fork is drawn first and a knife is drawn second is the product of these two individual probabilities, i.e. 2/3 x 6/17. What do you get?

  6. anonymous
    • one year ago
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    Do i cross multiply or go straight across?

  7. anonymous
    • one year ago
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    To multiply fractions, multiply the numerators together and multiply denominators together

  8. anonymous
    • one year ago
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    12 over 14 ?

  9. anonymous
    • one year ago
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    Not quite.\[\frac{ 2 }{ 3 } \times \frac{ 6 }{ 17 } = \frac{ 2 \times 6 }{ 3 \times 17 } = ?\]And don't forget to reduce the answer to lowest terms.

  10. anonymous
    • one year ago
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    OH, duh for me, 12/21. Sorry :p

  11. anonymous
    • one year ago
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    Nope. Try again. Use a calculator.

  12. anonymous
    • one year ago
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    I think

  13. anonymous
    • one year ago
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    What's 3 x 17 ?

  14. anonymous
    • one year ago
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    Wait i thought we were timing 7 times 3?

  15. anonymous
    • one year ago
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    Where does the 7 come from? The denominator is 3 x 17

  16. anonymous
    • one year ago
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    i AM SO SORRY. Rough morning. okay so 17 times 3 is 51 so its 12/51?

  17. anonymous
    • one year ago
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    Very good. But this can be reduced. 3 is a common factor, so divide both numerator and denominator by 3. What do you get?

  18. anonymous
    • one year ago
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    4/17?

  19. anonymous
    • one year ago
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    Excellent. So the probability of choosing a fork first and then a knife is 4/17. But we're not done yet. Do you know why?

  20. anonymous
    • one year ago
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    Ummm, well I dont think it can be simplified further... So i'm not really sure. Because it wants to know the probability that they are different??(Again sorry, rough morning an im horrible at math)

  21. anonymous
    • one year ago
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    No problem. You're right that it can't be simplified further. But, there is another possibility that satisfies the question. The question asks for the probability that the two choices will be different, and you calculated the probability of choosing a fork, then a knife. But what about choosing a knife first, then a fork. You also need to calculate that probability. Understand?

  22. anonymous
    • one year ago
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    Yes, but i thought it would just switch the fractions that we multiplied around and i would get the same answer

  23. anonymous
    • one year ago
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    Maybe, but let's go through it.

  24. anonymous
    • one year ago
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    So, what's the probability of choosing a knife out of the box first?

  25. anonymous
    • one year ago
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    6/17

  26. anonymous
    • one year ago
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    Remember, when you begin, there are 18 utensils in the box. Try again.

  27. anonymous
    • one year ago
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    6/18 which simplifies to 1/3

  28. anonymous
    • one year ago
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    Exactly. Now, there are 17 utensils in the box. What's the probability of choosing a fork second?

  29. anonymous
    • one year ago
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    12/17

  30. anonymous
    • one year ago
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    Correct. Now, the probability of choosing knife then fork is the product of these two probabilities. What do you get?

  31. anonymous
    • one year ago
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    12/51

  32. anonymous
    • one year ago
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    Excellent. Now, 3 is also a common factor so this fraction can be reduced, to what?

  33. anonymous
    • one year ago
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    6/17

  34. anonymous
    • one year ago
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    Not quite. What's 12 divided by 3?

  35. anonymous
    • one year ago
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    oh, 4 sorry

  36. anonymous
    • one year ago
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    Right. So now you have everything you need. Notice that the probabilities for the two possibilities ended up the same but the individual fractions were not simply reversed. So you can't assume things, you must go through and do the calculations.

  37. anonymous
    • one year ago
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    Alright, now to answer the question. You've determined that the probability of choosing a fork first and a knife second is 4/17. AND, you've determined that the probability of choosing a knife first and a fork second is 4/17. Thses are the only two scenarios that satisfy the question. So the final answer is the SUM of these two probabilities. What is it?

  38. anonymous
    • one year ago
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    So I got 8/34 but i feel like thats wrong

  39. anonymous
    • one year ago
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    Sorry. That's not it. Remember, we're not multiplying fractions here, we're adding them. When adding fractions with a common denominator, keep the denominator the same and add the numerators. For example,\[\frac{ 1 }{ 5 } + \frac{ 3 }{ 5 } = \frac{ 4 }{ 5 }\]

  40. anonymous
    • one year ago
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    2/6 which simplifies to 1/3???

  41. anonymous
    • one year ago
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    Nope. I'll write it out.\[\frac{ 4 }{ 17 } + \frac{ 4 }{ 17 } = ??\]

  42. anonymous
    • one year ago
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    Keep the denominator the same and add the numerators.

  43. anonymous
    • one year ago
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    8/17

  44. anonymous
    • one year ago
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    Bingo! That's your answer. Good job.

  45. anonymous
    • one year ago
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    Thank you

  46. anonymous
    • one year ago
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    You're welcome.

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