Find the Probability Error: Probability is an area of mathematics that is often misunderstood, leading to many surprising results as well as serious consequences. Describe how math is misused in the situation.

The Two Child Problem:

1. Mr. Smith has two children. The older child is a boy. What is the probability that both children are boys?

2. Mr. Smith has two children. At least one of them is a boy. What is the probability that both children are boys?

These are very close to the same problem. Are the answers the same?

Note: this problem assumes sex and gender are binary (50% chance of boy, 50% chance of girl). In reality, gender and sex are not binary. Can you think of a way to state a mathematically equivalent problem using something with a true 50-50 probability?