Multiplication Rule for Dependent Events

We use the multiplication rule for dependent events if the order of events is essential.

Formula:

P(A 1st and B 2nd) = P(A) * P(B|A)

• P(A 1st and B 2nd) - the probability of event A occurring first and event B occurring second,
• P(A) - the probability of event A occurring,
• P(B|A) - the probability of event B occurring after event A occured.

Task example:

You have a basket with 5 yellow and 15 blue balls. What is the probability that we will take the blue ball after the yellow?

1. P(yellow) = 5/20 = 0.25 = 25%,
2. P(blue|yellow) = 15/19 = 0.78947 = 78.947% (we tool one yellow ball, so, only 19 left),
3. P(yellow and blue|yellow) = P(yellow) * P(blue|yellow) = 25% * 78.947% = 19.737%