条件概率简介
通过示例理解概率和条件概率的基本概念。
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
掷两颗骰子得到的取值
| Die rolls | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 6 | 7 | 8 | 9 | 10 | 11 | 12 |
P(\text{sum of 7}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{6}{36} = \frac{1}{6} \approx 0.166
P(A|B) = \frac{P(A \cap B)}{P(B)}
P(B) = \frac{\text{Number of red cards}}{\text{Total number of cards}} = \frac{26}{52} = \frac{1}{2}
P(A \cap B) = \frac{\text{Number of hearts}}{\text{Total number of cards}} = \frac{13}{52} = \frac{1}{4}
P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{1}{4}}{\frac{1}{2}} = \frac{1}{2}
P(B) = \frac{\text{Number of students who play sports}}{\text{Total number of students}} = \frac{300}{500} = \frac{3}{5}
P(A \cap B) = \frac{\text{Number of students in both sports and choir}}{\text{Total number of students}} = \frac{150}{500} = \frac{3}{10}
P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{3}{10}}{\frac{3}{5}} = \frac{1}{2}