Question

Worldwide, the proportion of babies who are boys is about 0.51. A couple hopes to have 3 children, and we assume that the sex of each child is independent of the others. Let the random variable X represent the number of girls in the three children, so X might be 0, 1, 2, or 3. Give the probability function for each value of X. Round your answers to three decimal places.

Probability of X = 0: Enter your answer here
Probability of X = 1: Enter your answer here
Probability of X = 2: Enter your answer here
Probability of X = 3: Enter your answer here

Answer 1

The probability function for the random variable X, which represents the number of girls in three children given the worldwide proportion of boys, is calculated for each of the possible values of X, showing the chance of having zero, one, two, or all girls in a family of three children.

Step-by-step explanation:

The question involves determining the probability function for the random variable X, which represents the number of girls in three children, given that the worldwide proportion of babies who are boys is about 0.51. The random variable X can take on values 0, 1, 2, or 3.

Here is how to calculate the probabilities:

Probability of X = 0 (no girls, all boys): This is the probability of having all boys, which is (0.49)^3 = 0.117649, rounded to three decimal places is 0.118Note that the probability of having a boy is 1 - 0.51 = 0.49, which has been used in the calculations above.