Chapter 2 - Probability
Concepts
- Basics of probability
- Calculating conditional probabilities using tree diagrams, the counting method, or Bayes' Equation
- PDFs and CDFs and using them to calculate probabilities
- Differences in discrete and continuous data
- Moments of data focusing on the first and second moment
- Uniform distributions
Exercises
Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.
1. If you have breast cancer there is a 92% chance a screening will find it. If you do not have breast cancer there is a 97.7% chance a screening will show you do not have it. 1.47% of women have breast cancer. If a test detects cancer, what is the probability the woman truly has cancer? Draw a tree diagram to solve the problem.
0.3737
2. If you have breast cancer there is a 92% chance a screening will find it. If you do not have breast cancer there is a 97.7% chance a screening will show you do not have it. 1.47% of women have breast cancer. If a test detects cancer, what is the probability the woman truly has cancer? Use the counting method to solve the problem.
0.3737. See the video for the explanation of the counting method.
3. If you have breast cancer there is a 92% chance a screening will find it. If you do not have breast cancer there is a 97.7% chance a screening will show you do not have it. 1.47% of women have breast cancer. If a test detects cancer, what is the probability the woman truly has cancer? Use the counting method to solve the problem.
0.3737. See the video for the explanation of Bayes Equation.
4. Of the next 20,000 strangers to touch my car only one of them will be a thief. When the thief touches my car there is a 99.9% chance the alarm will go off. If it is not a thief there is a 10% chance the alarm will go off. Given that I hear my car alarm, what is the probability it is a thief?
0.0005