small-logo

Problem Solving Classroom

Tips from a Master Teacher (This is a work in progress.)

Two-Kids Problem

Two-Kids Problem

Let's say that when a child is born, the probability of it being a girl is 0.5.

Out of all the two-child families in the world, I have randomly selected one family that has a golden retriever named Waldo. One of the two children is a girl. What is the probability that the other one is a girl?

Difficulty: 3/5

Keywords: probability, combinations

Solution
The Solution

This is a fun problem to discuss as a class because some students will adamantly argue that the probability is 0.5. They'll say that the probability doesn't change just because you know the sex of the other child.

There are four possible ways that these two children could have arrived in the world: b-b, b-g, g-b, and g-g. The fact that you know that one is a girl eliminates the b-b families. In 2 out of 3 of the other families, the other child is a girl. So, the probability is 2/3 or 66.7%.

If you like this problem, then also take a look at the Monty Hall Problem.

Article Topics

Other Puzzles

No Accounting for Taste
No Accounting for Taste

Difficulty: 2/5

Two Bikes & a Bird
Two Bikes & a Bird

Difficulty: 3/5

Math Puppies
Math Puppies

Difficulty: 2/5

Two-Kids Problem
Two-Kids Problem

Difficulty: 3/5

Masked Man
Masked Man

Difficulty: 1/5

Delayed Donuts
Delayed Donuts

Difficulty: 2/5