IB DP Maths: AI HL复习笔记4.4.2 Conditional Probability
Conditional Probability
What is conditional probability?
- Conditional probability is where the probability of an event happening can vary depending on the outcome of a prior event
- The event A happening given that event B has happened is denoted A|B
- A common example of conditional probability involves selecting multiple objects from a bag without replacement
- The probability of selecting a certain item changes depending on what was selected before
- This is because the total number of items will change as they are not replaced once they have been selected
- The probability of selecting a certain item changes depending on what was selected before
How do I calculate conditional probabilities?
- Some conditional probabilities can be calculated by using counting outcomes
- Probabilities without replacement can be calculated like this
- For example: There are 10 balls in a bag, 6 of them are red, two of them are selected without replacement
- To find the probability that the second ball selected is red given that the first one is red count how many balls are left:
Worked Example
In a class of 30 students: 19 students have a dog, 17 students have a cat and 11 have both a dog and a cat. One student is selected at random.
a)Find the probability that the student has a dog.
b)Find the probability that the student has a dog given that they have a cat.
c)Find the probability that the student has a cat given that they have a dog.
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