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jesusfreak

  • 3 years ago

the principal will randomly choose 6 students from a large school to represent the school in a newspaper photograph. the probability that a chose student is an athlete is 30%. (assume that this doesn't change) What is the probability that 4 athletes are chosen?

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  1. ktklown
    • 3 years ago
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    Is this for a statistics class, or something like algebra?

  2. jesusfreak
    • 3 years ago
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    Algebra 2

  3. ktklown
    • 3 years ago
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    YTheManifold: that's not actually correct because you're not including the degree of freedom that any 4 can be chosen

  4. jesusfreak
    • 3 years ago
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    Would you like to see what the possible answers could be?

  5. YTheManifold
    • 3 years ago
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    Sorry \[ {6\choose 4}\cdot 0.3^4\cdot 0.7^2 \] of course

  6. ktklown
    • 3 years ago
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    .3^4 * .7^2 is the p^k and p^(n-k) but you need the (6 choose 4) as well.

  7. ktklown
    • 3 years ago
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    the formula YTheManifold just posted is correct - can you compute that, jesusfreak?

  8. cwrw238
    • 3 years ago
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    yes - this a Binomial Probability distribution

  9. ktklown
    • 3 years ago
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    the general form is (n choose k) * p^k * p^(n-k). (typo in the previous one)

  10. jesusfreak
    • 3 years ago
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    It all looks like gibberish. I have no idea what to do.

  11. jesusfreak
    • 3 years ago
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    The answers it gives is 0.05, 0.06, 0.07, 0.08

  12. ktklown
    • 3 years ago
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    OK, let's go through it step by step. Do you know how to compute .3^4?

  13. cwrw238
    • 3 years ago
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    th 6 4 part means the number combinations of 4 from 6

  14. jesusfreak
    • 3 years ago
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    Yeah it's 81

  15. ktklown
    • 3 years ago
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    You forgot the decimal -- it's 0.3^4 we're computing. Then multiply that by 0.7^2.

  16. jesusfreak
    • 3 years ago
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    ok it equals .003969

  17. ktklown
    • 3 years ago
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    yes! Now you just need to multiply that by the (6 4) part, and you'll be done. That's called a "binomial". It's pronounced "6 choose 4", which means, if you have 6 things, how many ways can you choose 4 of them?

  18. ktklown
    • 3 years ago
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    There's a formula for computing that, but a lot of people just type it into a calculator - it's 15 in this case.

  19. ktklown
    • 3 years ago
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    The formula is n! / ( k! * (n-k)! )

  20. ktklown
    • 3 years ago
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    Anyway so in this case just multiply 15 * .3^4 * .7^2 and that's your answer.

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