Example 1: The joint probability of events A and B is 15% with the probability of event A being 40% and the probability of event B being 50%. What is the conditional probability of event A given that event B has occurred?

Example 2: The conditional probability of event A given that event B has occurred is 30% with the probability of event A being 40% and the probability of event B being 50%. What is joint probability of events A and B? Are events A and B mutually exclusive?

Example 3: Suppose we flip a coin 3 times (i.e. N=3). Consider heads as "success". Determine the probability of obtaining 3, 2, 1 and 0 heads.