Question

an experiment consists of observing the genders and birth orders in three-child families. assume all eight outcomes have the same probability of occurring. (a) what is the probability that a family has at least two boys?

Answer 1

The probability that a three-child family has at least two boys is 4 out of 8, which simplifies to 1/2 or 50%.

Step-by-step explanation:

The question is asking for the probability that a three-child family has at least two boys.

To solve this, we'll need to calculate the complement probability — that is, the probability of having fewer than two boys — and subtract it from 1.

The outcomes for three-child families, with regards to gender, are: BBB, BBG, BGB, GBB, BGG, GBG, GGB, and GGG; where 'B' represents a boy and 'G' represents a girl.

If we count the scenarios with at least two boys, we have 4 outcomes (BBB, BBG, BGB, GBB).

Since each outcome is equally likely, and there are a total of 8 outcomes, the probability of having at least two boys is simply the number of favorable outcomes (at least two boys) divided by the total number of outcomes.

This gives us a probability of 4/8 or 1/2.