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Math Help - Introduction to probability, please check my answers.

  1. #1
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    Introduction to probability, please check my answers.

    1.In how many diff. ways can a committee of 5 be selected from 62 members of a clinical staff.
    5/62 *100 = 8.06%

    2.In how many ways can a director of a research lab choose 2 chemists among 7 other applicants and 3 physicist from the applicants.
    Chemist:2/7*100=28.57%
    Physicist:3/7*100=42.86%

    3.What is the possibility of drawing an ace from a well shuffled deck of 52 playing cards.
    4/52*100=7.7%

    4.If 3 of 20 tires are defective and 4 of them are randomly chose for inspection, what is the probability that 1 of the defective tires will be included.
    3/20=.15 4/.15=26.67.

    Any help will be appreciated, thank you
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  2. #2
    Member
    Joined
    Mar 2009
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    133
    Hello,

    You need to learn about combinations -
    (1) number of ways to select 5 from 62 is;
    62C5=\frac{62!}{5!\cdot 57!}=6471002

    (2) Im not sure of the question, from the 7 applicants, how many are chemists, and how many are physicists?

    (3) Correct

    (4) You are choosing 4 tyres from 20. You want the probability that 1 of the chosen tyres is defective, so if you let N mean not defective, and D defective, then you have the following;
    DNNN, NDNN, NNDN, NNND. Each of these scenarios have the same probability of occuring, so the probability of selecting 1 defective from a sample of 4 is;
    \frac{3}{20} \cdot \frac{17}{19} \cdot \frac{16}{18} \cdot \frac{15}{17} \cdot 4 = 0.421053
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