IB DP Maths: AA SL复习笔记4.3.2 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

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:

How do I tell if two events are independent using conditional probabilities?

This is given in the formula booklet