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A family has three children. If the genders of these children are listed in the order they are born, there are eight possible outcomes: BBB, BBG, BGB, BGG, GBB, GBG, GGB, and GGG. Assume these outcomes are equally likely. Let X represent the number of children that are girls. Find the probability distribution of X.

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Answer:

P(X = 0) = 1/8

P(X = 1) = 3/8

P(X = 2) = 3/8

P(X = 3) = 1/8

Step-by-step explanation:

The family may have zero, one, two or three children that are girls (X = 0, 1, 2, 3).

Out of the 8 possible outcomes for having three children, there is 1 with zero girls,  3 with one girl, 3 with two girls, and 1 with 3 girls. The probability distribution of X is:

P(X = 0) = 1/8

P(X = 1) = 3/8

P(X = 2) = 3/8

P(X = 3) = 1/8

The probability distribution of X is

P(X = 0) =[tex]1\div 8[/tex]

P(X = 1) = [tex]3\div 8[/tex]

P(X = 2) =[tex]3\div 8[/tex]

P(X = 3) = [tex]1\div 8[/tex]

Calculation of the probability:

Since the family may have zero, one, two or three children that are girls (X = 0, 1, 2, 3).

So,

Out of the 8 possible outcomes for having three children, there is 1 with zero girls,  3 with one girl, 3 with two girls, and 1 with 3 girls. So the above should be the probability

Learn more about number here: https://brainly.com/question/17389085

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