Introduction to Probability · 免费预览
计数中的故事证明与补集
通过讲述同一个故事来对恒等式的两边进行计数，并在实际问题上运用补集法及其他计数策略。
1. Story proofs
Story proofs
2. Complements and other counting strategies
Complements and other counting strategies
3. Putting the toolkit to work
Putting the toolkit to work
4. A story proof recognized
The identity n times Binomial(n-1, k-1) = k times Binomial(n, k) counts a single collection. Which one?
5. Complement counting
Among all 5-card hands from a 52-card deck, how do you most cleanly count hands that contain at least one heart?
6. Balls into boxes
How many ways can 7 identical candies be distributed among 4 children? Stars and bars applies. Enter the integer.
7. Exactly two women on the committee
A committee of 3 is chosen from 4 women and 4 men. The probability of exactly two women is Binomial(4,2) times Binomial(4,1) divided by Binomial(8,3). Write it as a fraction in lowest terms and enter the denominator.
8. A full house count
A poker full house is three cards of one rank and two of another, like three queens and two sixes. How many full house hands exist? Enter the integer.
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.