1. What is Conditional Probability?
Conditional Proababilty comes up when it is given that something has already happened. We use conditional probability for dependent events, where one event affects the another.
1.1 AND Rule for Conditional Probability
It states that for two dependent events A and B,
P(A and B) = P(A) x P(B given A)
The probability if two dependent events A and B happening together is equal to the probability of event A times the probability of event B when event A has happened.
Look at the examples below to understand how to apply the above rule.
Example: The probability that Ryan loses the first running race is 0.4. If he wins the first race, the probability of him winning the second race is 0.6.
What is the probability than Ryan wins both the races?
Example: From a deck of playing cards, two cards are drawn at random without replacement. What is the probability that both the cards drawn are Kings?
2. Calculating Condtional Probability using Tree diagrams
As the probabilities on the sets of branches in tree diagrams change, depending on the previous event, its a great way to deal with questions on Conditional Probability using tree diagrams.
Example: A bag contains 7 blue marbles and 4 green marbles. Two marbles are taken from the bag at random without replacement. Find the probability that both the marbles are of different color.
