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Math Help - Sample Spaces and Events

  1. #1
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    Unhappy Sample Spaces and Events

    43. From a group of 20 men and 16 women, 2 people are chosen at random. Find the probability of:

    a) 1 man and 1 woman being chosen
    b) 2 men being chosen
    c) 2 women being chosen

    Thank you
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  2. #2
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    a. 1 man being chosen = 20/36 and 1 woman being chosen is 16/36

    The probability of both would be the product of the two probabilities I believe.


    b. The probability of the first man being chosen is 20/36 and the probability of the second is 19/35 since you are now one man down. Multiply the two probabilities.


    c. The probability of the first woman being chosen is 16/36 and the second is 15/35. Multiply the two like above.
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  3. #3
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    Quote Originally Posted by toop View Post
    a. 1 man being chosen = 20/36 and 1 woman being chosen is 16/36

    The probability of both would be the product of the two probabilities I believe.


    b. The probability of the first man being chosen is 20/36 and the probability of the second is 19/35 since you are now one man down. Multiply the two probabilities.


    c. The probability of the first woman being chosen is 16/36 and the second is 15/35. Multiply the two like above.
    I don't think your solution to (a) is correct.

    The correct answer is given by \frac{{20 \choose 1} \cdot {16 \choose 1}}{{36 \choose 2}} = \frac{20 \cdot 16 \cdot 2}{36 \cdot 35} \, ....
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