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Math Help - reivew for final

  1. #1
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    reivew for final

    Please check my answers, if any of these is not correct, please help. Thank you very much.

    Three marbles are drawn at random from an urn containing 8 black, 7 white, and 5 red marbles.
    What is the probability that none of them are white. Answer: \frac{_{13}C_3}{_{20}C_3}.
    What is the probability that at least one of them is red? Answer: 1-\frac{_{15}C_3}{_{20}C_3}

    A drawer contains 8 blue socks, 4 green socks, and 6 brown socks. If you choose 2 socks at random, what is the probability that they are both brown? Answer: \frac{_{6}C_2}{_{18}C_2}

    On a 10-questions true-false test, the questions are answered at random. What is the probability of answering at least 8 questions correctly? Answer: .5^8+.5^9+.5^{10}

    Three letters are chosen at random from the word POSTER. What is the probability that the selection will contain E or O or both?
    Please help me with this one.
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  2. #2
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    Quote Originally Posted by dori1123 View Post

    On a 10-questions true-false test, the questions are answered at random. What is the probability of answering at least 8 questions correctly? Answer: .5^8+.5^9+.5^{10}

    Three letters are chosen at random from the word POSTER. What is the probability that the selection will contain E or O or both?
    Please help me with this one.
    Hi!

    For the 2nd last question, I think it should be:
    Let X be the no. of correct answers:
    P(X \geq 8)= {10 \choose 8}(0.5)^8(0.5)^2+ {10 \choose 9}(0.5)^9(0.5)+(0.5)^{10}

    Last question:
    Consider the case when there are no E or O:
    P(\textrm{no E or O or both})=\frac{{4 \choose 3}}{{6 \choose 3}}
    Then take the complement
    P(\text{contain E or O or both})=1-\frac{{4 \choose 3}}{{6 \choose 3}}
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  3. #3
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    Hello, Dori!

    Your "marbles" and "socks" answers are correct.


    On a 10-questions true-false test, the questions are answered at random.
    What is the probability of answering at least 8 questions correctly?
    This is a Binomial Probability problem . . .

    . . \begin{array}{ccc}\text{8 right, 2 wrong:} & _{10}C_8\,(0.5)^8\,(0.5)^2 \\ \text{9 right, 1 wrong:} & _{10}C_9\,(0.5)^9\,(0.5)^1 \\ \text{10 right, 0 wrong:} & _{10}C_{10}\,(0.5)^{10}\,(0.5)^0 \end{array}

    And add them up . . .




    Three letters are chosen at random from the word POSTER.
    What is the probability that the selection will contain E or O or both?
    From your work on the other two problems, you should have nailed this one.


    There are: . _6C_3 possible outcomes.

    How many outcomes contain no E's or O's?
    . . There are: . _4C_3 of them.

    Therefore: . P(\text{E or O or both}) \;=\;1 - \frac{_4C_3}{_6C_3}

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