Introduction to Probability · 免费预览
概率：从等可能性到公理
等可能性下概率的定义、其性质，以及将概率推广到任意样本空间的公理。
1. The naive definition
The naive definition
2. Properties that follow from symmetry
Properties that follow from symmetry
3. The axioms of probability
The axioms of probability
4. Why axioms beat intuition
Why axioms beat intuition
5. When the naive definition applies
A jar holds 3 red and 5 blue marbles, identical except for color, and one is drawn blind. Does the naive definition of probability apply to the color of the drawn marble?
6. Complements versus unions
A fair coin is tossed 4 times. Which expression computes P(at least one tail)?
7. Aces or hearts
One card is drawn from a well-shuffled deck. Using inclusion-exclusion, P(ace or heart) = P(ace) + P(heart) - P(ace of hearts). Write the result as a fraction a/b in lowest terms, for example 7/13. Enter the denominator b.
8. A weighted die
A die is loaded so that and the other five faces are equally likely. What is the probability of rolling a number strictly less than 5? Enter a decimal like 0.4.
9. Monotonicity check
An event A is contained in an event B, and P(A) = 0.3 while P(B) = 0.3. What is P(B and not A)? Enter a decimal.
10. In your own words
In your own words, state the most important definition, theorem or method of this lesson and explain what it says.