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