Math Problem Statement
In a family with 3 children, excluding multiple births, what is the probability of having 2 boys and 1 girl, in that order? Assume that a boy is as likely as a girl at each birth. How will your answer change if any order is allowed?
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Combinations
Permutations
Formulas
P(Boy, Boy, Girl) = (1/2) * (1/2) * (1/2) = 1/8
Number of ways to arrange 2 boys and 1 girl: C(3, 2) = 3
P(2 boys, 1 girl in any order) = 3 * (1/8) = 3/8
Theorems
Basic Probability Rule
Combination Formula: C(n, k) = n! / (k!(n - k)!)
Suitable Grade Level
Grades 6-8