# Children’s Gender. A certain couple is equally likely to have either a boy or a girl. If the family has four children, let X denote the number of girls.a. Identify the possible values of the random variable X.b. Determine the probability distribution of X. (Hint: There are 16 possible equally likely outcomes. One is GBBB, meaning the first born is a girl and the next three born are boys.)Use random-variable notation to represent each of the following events. Also use the special addition rule and the probability distribution obtained in part (b) to determine each event’s probability. The couple hasc. exactly two girls.d. at least two girls.e. at most two girls.f. between one and three girls, inclusive.g. children all of the same gender.

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Children’s Gender. A certain couple is equally likely to have either a boy or a girl. If the family has four children, let X denote the number of girls.

a. Identify the possible values of the random variable X.
b. Determine the probability distribution of X. (Hint: There are 16 possible equally likely outcomes. One is GBBB, meaning the first born is a girl and the next three born are boys.)

Use random-variable notation to represent each of the following events. Also use the special addition rule and the probability distribution obtained in part (b) to determine each event’s probability. The couple has

c. exactly two girls.
d. at least two girls.
e. at most two girls.
f. between one and three girls, inclusive.
g. children all of the same gender.

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Step 1

Note:

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a.

The random variable X denotes the number of girls, if the family has four children and each couple is equally likely to have a boy or a girl.

Since the family has four children, the possible values that the random variable X can take are X=0,1,2,3,4.

Step 2

b.

Obtain the probability distribution of the random variable X:

Since, the family has four children and a certain couple is equally likely to have either a boy or a girl, the sample space contains the following outcomes.

Step 3

The probability distribution for the random varia...

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