A family has four children. If the genders of these children are listed in the o

Question

A family has four children. If the genders of these children are listed in the order they are born, there are sixteen possible outcomes: BBBB, BBBG, BBGB, BGBB, GBBB, BGBG, GBGB BGGB, GBBG, BBGG, GGBB, BGGG, GBGG, GGBG, GGGB, and GGGG. Assume these outcomes are equally likely. Let.X represent the number of children that are girls. Find the probability distribution of X. Part 1 out of 2 Find the number of possible values for the random variable X. There arepssible values for the random variable X.

Explanation / Answer

In this case there are four children and the random variable X counts the number of girls for each possilbe outcome.

Since there are four children, there can be atmost 4 girls and atleast 0 girls. So the possible values for X are 0,1,2,3 and 4.

There are 5 possible values for the random variable X.

P(X=0) = 1/16

P(X=1) = 4/16

P(X=2) = 6/16

P(X=3) = 4/16

P(X=4) = 1/16

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