Multiplication Rule for Independent Events

When do we use the multiplication rule?

If we want to calculate the probability of two events occur at the same time (event A and B), we use multiplication rule.

Formula:

P(A and B) = P(A) * P(B)

• P(A and B) - the probability of event A occurring and event B occurring at the same time,
• P(A) - the probability of event A occurring,
• P(B) - the probability of event B occurring.

Task example:

If you are rolling two dice simultaneously, what is the probability that the outcome of the first one is an even number and the second is 5?

The outcomes for the first case (even number): 2, 4, 6.

The outcomes for the second case (number 5): 5.

1. P(even) = 3/6 = 0.5 = 50%,
2. P(5) = 1/6 = 0.1667 = 16.67% (ronded to the two decimal points),
3. P(even and 5) = P(even) * P(5) = 0.0833 = 8.33%