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anonymous

  • one year ago

I worked the probability problem I just need someone to check the answer please! In a batch of 50 batteries, four are defective. If we select 3 batteries, what is the probability that at least 2 are good.

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  1. anonymous
    • one year ago
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    I did P=1-P(0 good)P(1good) my answer is 99%

  2. amistre64
    • one year ago
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    4 out of 50 are bad, so 46 out of 50 are good can we do a binomial approach?

  3. amistre64
    • one year ago
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    \[\binom{50}{2}(\frac{46}{50})^2(\frac{4}{50})^{48}+\binom{50}{3}(\frac{46}{50})^{3}(\frac{4}{50})^{47}\]

  4. amistre64
    • one year ago
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    i think 50s are 3 in the binomial code ...

  5. anonymous
    • one year ago
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    a binomial approach is used when looking for the probability of an exact number of things. i used the multiplication rule( that is what is used in the book to find at least prob.)

  6. amistre64
    • one year ago
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    \[\binom{3}{2}(\frac{46}{50})^2(\frac{4}{50})^{1}+\binom{3}{3}(\frac{46}{50})^{3}(\frac{4}{50})^{0 }\]

  7. amistre64
    • one year ago
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    exactly 2 or exactly 3 are at least 2

  8. anonymous
    • one year ago
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    P(at least 2 good)=1-69/4900*1/4900 =.999999 =99%

  9. anonymous
    • one year ago
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    P( 0 good) = ((4c3)(46c0))/(50c3) =1/4900

  10. amistre64
    • one year ago
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    it is a high number ... im getting 98.2 or so

  11. anonymous
    • one year ago
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    P(1 good)= ((4c2)(46c1))/(50c3) =69/4900

  12. amistre64
    • one year ago
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    shold we assume replacement or not? ggb = (4*46*47)/(50*49*48) gbg = (4*46*47)/(50*49*48) bgg = (4*46*47)/(50*49*48) ggg = (46*47*48)/(50*49*48)

  13. anonymous
    • one year ago
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    no replacement

  14. amistre64
    • one year ago
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    3*(4*46*47)/(50*49*48)+(46*45*44)/(50*49*48) without replacement gets us about 99.51

  15. anonymous
    • one year ago
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    So in other words 99% would be a correct answer

  16. amistre64
    • one year ago
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    im not the one grading it, but it seems fair enough :)

  17. anonymous
    • one year ago
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    Thanks!

  18. amistre64
    • one year ago
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    youre welcome

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