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Math Help - probaility Question

  1. #1
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    probability Question

    Please any one explain me,as soon as possible how to get answer for below question.Any help really appreciated.Thank you.

    A family of five children is known to have at least two girls. What is the probability of this family having exactly four girls?

    Choose at least one answer.

    a. 5/30
    b. 5/26
    c. 8/10
    d. 5/10
    e. 11/30
    Last edited by lasantha; August 6th 2010 at 01:37 AM. Reason: spelling misake
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  2. #2
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    It is not impossible to list all possiblities. Since each child can be either boy or girl there are 2^5= 32 possibilities: BBBBB, BBBBG, BBBGB, etc.

    Rather than do that, I will note that exactly one has no girls: BBBBB. Five have one girl: GBBBB, BGBBB, BBGBB, BBBGB, and BBBBG. That leaves 32- 6= 26 that have two or more girls. Therefore, your answer will be a fraction having 26 as denominator, not 32.

    It should be easy to see that there are also exactly five ways to list "four girls": BGGGG, GBGGG, GGBGG, GGGBG, and GGGGB.
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  3. #3
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    Quote Originally Posted by lasantha View Post
    Please any one explain me,as soon as possible how to get answer for below question.Any help really appreciated.Thank you.

    A family of five children is known to have at least two girls. What is the probability of this family having exactly four girls?

    Choose at least one answer.

    a. 5/30
    b. 5/26
    c. 8/10
    d. 5/10
    e. 11/30
    Here is an alternative way.

    The only possibilities are... 2 girls and 3 boys, 3 girls and 2 boys, 4 girls and 1 boy, 5 girls

    Therefore, the probability of exactly 4 girls is

    \frac{number\ of\ ways\ to\ have\ 4\ girls}{number\ of\ ways\ to\ have\ 2,\ 3,\ 4\ or\ 5\ girls}

    =\displaystyle\huge\frac{\binom{5}{4}}{\binom{5}{2  }+\binom{5}{3}+\binom{5}{4}+\binom{5}{5}}

    =\frac{5}{10+10+5+1}
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