Introduction to Probability · 免费预览
条件概率与鹅卵石世界直觉
证据到来时如何更新概率：条件概率的定义、其卵石世界图景，以及为什么已知 A 时 B 的概率不同于已知 B 时 A 的概率。
1. Evidence shrinks the world
Evidence shrinks the world
2. Computing with the definition
Computing with the definition
3. Conditional probability as a probability measure
Conditional probability as a probability measure
4. Reading conditional from a table
In the class survey above, 120 students study calculus, of whom 72 study physics; of the 80 who do not study calculus, 24 study physics. What is P(studies calculus given studies physics)?
5. Which conditional is wanted
A screening test for a rare disease correctly lights up 99 percent of sick people. A journalist writes that a positive result means a 99 percent chance of disease. What is swapped?
6. Condition on the first die
Two fair dice are rolled. Given that the first die shows 3, what is the probability that the total is at least 7? Write the answer as a fraction a/b in lowest terms and enter b.
7. The reversed fraction
In a company, 30 percent of employees code and 20 percent code AND design. Among coders, what fraction design? Enter a decimal like 0.67.
8. Evidence that rules out outcomes
Three coins are tossed. Given that at least one shows heads, what is the probability that all three show heads? Enter a fraction like 1/7.
9. In your own words
In your own words, state the most important definition, theorem or method of this lesson and explain what it says.