Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
4. Probability
Multiplication Rule: Independent Events
Problem 4.3.6
Textbook Question
Probability of a Girl Assuming that boys and girls are equally likely, find the probability of a couple having a boy when their third child is born, given that the first two children were both girls.

1
Step 1: Understand the problem. The question asks for the probability of the third child being a boy, given that the first two children are girls. Note that the genders of the children are independent events, meaning the outcome of one child does not affect the outcome of another.
Step 2: Recall the basic probability rule. When boys and girls are equally likely, the probability of having a boy or a girl for any single child is 1/2 (or 0.5).
Step 3: Recognize that the condition provided (the first two children being girls) does not influence the probability of the third child’s gender. This is because the events are independent.
Step 4: Write the probability of the third child being a boy as P(Boy) = 1/2. This is based solely on the fact that boys and girls are equally likely, and the previous outcomes do not affect this probability.
Step 5: Conclude that the probability of the third child being a boy remains 1/2, regardless of the genders of the first two children. This is a key concept in understanding independent events in probability.

This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Conditional Probability
Conditional probability refers to the likelihood of an event occurring given that another event has already occurred. In this scenario, we are interested in the probability of having a boy as the third child, given that the first two children were girls. This concept is crucial for understanding how prior outcomes can influence the probability of future events.
Recommended video:
Introduction to Probability
Independence of Events
In probability, two events are considered independent if the occurrence of one does not affect the occurrence of the other. In this case, the gender of the third child is independent of the genders of the first two children. This means that regardless of the first two being girls, the probability of the third child being a boy remains unchanged.
Recommended video:
Probability of Multiple Independent Events
Sample Space
The sample space is the set of all possible outcomes of a probabilistic experiment. For the birth of children, the sample space consists of combinations of boys and girls. In this problem, the relevant outcomes for the third child are 'boy' or 'girl', and understanding the sample space helps clarify the probabilities associated with each outcome.
Recommended video:
Sampling Distribution of Sample Proportion
Watch next
Master Probability of Multiple Independent Events with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice