A couple plans to have 3 kids. There are 8possible arrangements of girls and boy

Question

A couple plans to have 3 kids. There are 8possible arrangements of girls and boys. For example, GGBmeans the first two kids are girls and the third kid is aboy. All 8 arrangements are (approximately) equallylikely.(a.)Write down all 8 arrangements of the sexes of 3kids. What is the proability of any one of thesearrangements?
(b.) Let X be the number of girls the couple has. What is theprobability that X = 2?
(c.) Starting from your work in (a), find the distribution ofX. That is, what values can X take, and what are theprobabilities for each value? A couple plans to have 3 kids. There are 8possible arrangements of girls and boys. For example, GGBmeans the first two kids are girls and the third kid is aboy. All 8 arrangements are (approximately) equallylikely.(a.)Write down all 8 arrangements of the sexes of 3kids. What is the proability of any one of thesearrangements?
(b.) Let X be the number of girls the couple has. What is theprobability that X = 2?
(c.) Starting from your work in (a), find the distribution ofX. That is, what values can X take, and what are theprobabilities for each value?

Explanation / Answer

a/ Possible outcomes: GGG GGB GBG GBB BGG BGB BBG BBB Probability for each outcome is 1/8 b/ X= # girls. From the above table, P(X=2) = 3/8 c/ Distribution of X (count the number of girls for eachoutcome and divide the total by 8) P(X=0) = 1/8 P(X=1) = 3/8 P(X=2) = 3/8 P(X=3) = 1/8

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