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kcla1996

  • 2 years ago

You have a 5-question multiple-choice test. Each question has four choices. You don’t know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly?

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  1. CliffSedge
    • 2 years ago
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    To get the experimental probability, you have to run the experiment.

  2. kcla1996
    • 2 years ago
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    can i just do it by writing a binomial

  3. CliffSedge
    • 2 years ago
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    Yes, this is a binomial situation.

  4. CliffSedge
    • 2 years ago
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    Consider the probability of success for each trial, the number of trials, the number of successes sought, and the number of combinations of getting that many successes.

  5. kcla1996
    • 2 years ago
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    10*9/4^3 this is what i got.....

  6. CliffSedge
    • 2 years ago
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    Mmm, some of those numbers are right, but aren't in the right places...

  7. satellite73
    • 2 years ago
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    exactly 3 right out of 5 means 3 right, 2 wrong and \(\dbinom{5}{2}\) ways to do it

  8. CliffSedge
    • 2 years ago
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    Number of ways to get 3 out of 5 = 5C3 = 5C2 = 10, so the 10 in right.

  9. CliffSedge
    • 2 years ago
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    ... *is right. 3 successes = (.25)^3 with a 25% chance of getting any question correct at random. 2 failures = (.75)^2 for similar reasons as above.

  10. kcla1996
    • 2 years ago
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    so can you help me write the answer?

  11. CliffSedge
    • 2 years ago
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    See http://stattrek.com/probability-distributions/binomial.aspx?Tutorial=Stat for derivation of the binomial formula.

  12. CliffSedge
    • 2 years ago
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    I think you have everything you need; just multiply it all together.

  13. kcla1996
    • 2 years ago
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    i really not get it.

  14. CliffSedge
    • 2 years ago
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    There are ten ways to get 3 out of 5. (use combinations formula 5choose3) To get 3 successes with a 25% chance each, that's 0.25 × 0.25 × 0.25 = (0.25)^3 To also get the 2 failures with a 75% chance: 0.75 × 0.75 = (0.75)^2 Altogether, the probability is 10 × (0.25)^3 ×(0.75)^2.

  15. kcla1996
    • 2 years ago
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    is 10 x (.25)^3 x(0.75)^2 the answer

  16. CliffSedge
    • 2 years ago
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    Makes sense to me. 10 ways to have 3 successes and 2 failures multiplied by the probability of having 3 successes multiplied by the probability of having 2 failures. See also http://stattrek.com/probability/probability-rules.aspx?Tutorial=Stat

  17. kcla1996
    • 2 years ago
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    but is it the answer

  18. CliffSedge
    • 2 years ago
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    Does it make sense to you? Why do you still have doubts? Follow those links to that website I posted and study until you understand why the probability is computed that way.

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