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    Simple Probability, Sample Spaces, Events

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    A couple has three children, assume the likelihood of a boy is the same as a girl:

    List sample space: {BBB,BBG,BGG,GGG}
    Event the children are grils: {GGG}
    Event the couple has one or more boy: {BBB,BBG,BGG}
    Probability all children are girls: 1/4
    Probability the couple has at least one boy: 3/4
    Probability the couple has exactly one boy: 1/4
    Probability that the couple has two childern of the same gender: 4/4
    Knowing that they have one boy, the probability that all the childeren are boys:1/3
    Knowing two children are the same gender the probability that they are all boys:1/4
    Knowing that two childern are the same gender, the probabilty they have at least two grils:2/4
    X -> Random variable of boys couple has -
    List all pssoible values of x {0,1,2,3}
    PMF of X: 1 = .25, 2 =.25, 3=.25
    CDF of X: 1 =.25, 2= .50, 3= .75
    Expected Value Of X = 1.5
    Expected Value Of X^2 = 3.5
    Variance X = 2
    Standard Deviation Of X = .42

    © BrainMass Inc. brainmass.com February 24, 2021, 3:20 pm ad1c9bdddf
    https://brainmass.com/math/probability/simple-probability-sample-spaces-events-73351

    Solution Preview

    A couple has three children, assume the likelihood of a boy is the same as a girl:

    (a) List sample space: {BBB,BBG,BGG,GGG}
    Correct! The sample space has 4 outputs.
    (b) Event the children are grils: {GGG}
    Correct!
    (c) Event the couple has one or more boy: {BBB,BBG,BGG}
    Correct!
    (d) Probability all children are girls: 1/4
    Correct! It is one case in (b) out of the 4 outputs in (a).
    (e) Probability the couple has at least one boy: 3/4
    Correct!. There are 3 cases in (c) out of the 4 ...

    Solution Summary

    Simple Probability, Sample Spaces, Events are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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