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Math Help - Probability

  1. #1
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    Probability

    A family with 5 children is selected at random.What is the probability that the family has at
    least 3 boys?
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  2. #2
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    Hello, Jhonson!

    A family with 5 children is selected at random.
    What is the probability that the family has at least 3 boys?
    Here's an "eyeball" solution . . .

    Of all the possible combinations of gender among five children,
    . . exactly HALF of them have more boys than girls.
    . . (And the other half has more girls than boys.)

    Therefore: . P(\text{3 or more boys}) \:=\:\frac{1}{2}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    A more "mathematical" solution . . .


    There are: . 2^5 = 32 possible sets of gender.


    How many have 3 boys and 2 girls?. . _5C_3 = 10

    How many have 4 boys and 1 girl?. . _5C_4 = 5

    How many have 5 boys?. . _5C_5 = 1


    Hence, there are: . 10 + 5 + 1 \:=\:16 cases with 3 or more boys.


    Therefore: . P(\text{3 or more boys}) \:=\:\frac{16}{32} \:=\:\frac{1}{2}

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