Question

a couple has three children. let x represent the number of girls. what is the probability the couple has no girls? give your answer to three decimal places.

x	proportion
1	0.375
2	0.375
3	0.125

Explanation:

Step1: Identify X for no girls

When there are no girls, \( X = 0 \). We need to find the proportion (probability) for \( X = 0 \). But first, recall that the sum of all probabilities in a probability distribution is 1. So we can calculate the missing probability for \( X = 0 \) by subtracting the sum of the other probabilities from 1.

Step2: Calculate sum of known probabilities

The known probabilities are for \( X = 1 \): \( 0.375 \), \( X = 2 \): \( 0.375 \), \( X = 3 \): \( 0.125 \). Sum them: \( 0.375 + 0.375 + 0.125 = 0.875 \).

Step3: Find probability for X=0

Subtract the sum from 1: \( 1 - 0.875 = 0.125 \).

Answer:

\( 0.125 \)