Example 1: Using multiplication rule to calculate joint probability
The probability of an increase in stock price is 40 percent if the interest rate rises by more than one percent. The probability of an increase in the interest rate by more than one percent is 30 percent. What is the joint probability that both events (increase in stock price and increase in interest rate by more than one percent) occur together?
The independent events are the events that are not dependent on the occurrence of the other event.
For independent events A and B: P(A|B) = P(A)
P(B|A) = P(B)
Therefore, P(AB) = P(A|B)*P(B)= P(A)*P(B)
The joint probability of independent events is equal to the product of the unconditional probabilities of those events.
For more than two independent events, P(ABCD) = P(A)*P(B)*P(C)*P(D)
The probability that at least one of two events A and B will occur is given by the additional rule as discussed previously and is given by the following formula.
P(A or B) = P(A) + P(B) - P(AB) = P(A) + P(B) - P(A|B)*P(B)