Question 6 • Concepts in Probability and Statistics
A family has two children. If cap b represents a boy and cap g represents a girl, the set of outcomes for the possible genders of the children is cap s is equal to BB, BG, GB, GG , with the oldest child listed first in each pair. Let cap x represent the number of times cap g occurs. Which of the following is the probability distribution, cap p sub cap x times x ?
Answer
A
Table with 2 columns and 4 rows.Row 1: Column 1, 'cap x'; Column 2, 'cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 2 5' Row 3: Column 1, '1'; Column 2, '0 point 7 5' Row 4: Column 1, '2'; Column 2, '0'
B
Table with 2 columns and 4 rows.Row 1: Column 1, 'cap x'; Column 2, 'cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0' Row 3: Column 1, '1'; Column 2, '0 point 5' Row 4: Column 1, '2'; Column 2, '0 point 5'
C
Table with 2 columns and 4 rows.Row 1: Column 1, 'cap x'; Column 2, 'cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 2 5' Row 3: Column 1, '1'; Column 2, '0 point 5' Row 4: Column 1, '2'; Column 2, '0 point 2 5'
D
Table with 2 columns and 4 rows.Row 1: Column 1, 'cap x'; Column 2, 'cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 3 3' Row 3: Column 1, '1'; Column 2, '0 point 3 3' Row 4: Column 1, '2'; Column 2, '0 point 3 3'
Explanation
The four possible outcomes, BB, BG, GB, and GG, are equally likely. The number of girls is 0 only for BB, 1 for BG or GB, and 2 only for GG. Therefore, the probabilities are 1/4 = 0.25, 2/4 = 0.5, and 1/4 = 0.25, respectively, matching the table with probabilities 0.25, 0.5, and 0.25.
AI-written and checked against the verified answer.