Multiplication Rule Statistics B Mr. Evans

Addition vs. Multiplication Rule The addition rule helped us solve problems when we performed one task and wanted to know the probability of two things happening during that task. The multiplication rule also deals with two events, but in these problems the events occur as a result of more than one task (rolling one die then another, drawing two cards, spinning a spinner twice, pulling two marbles out of a bag, etc).

The Multiplication Rule The probability of the event A occurring and then the event B occurring (separately) is:

Independent and Dependent Independent Events are events that are not affected by each other. When you flip a coin, the coin is independent for every flip Dependent Events are events that are affected by the outcome of the previous event. When you pick a marble out of a bag, it is dependent on the marble picked before

Guided Exercise #1 Suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, put it back in the box and draw another marble (with replacement). What is the probability of pulling out a red marble followed by a blue marble?

Guided Exercise #1 Consider the same box of marbles as in the previous example. However in this case, we are going to pull out the first marble, leave it out, and then pull out another marble. What is the probability of pulling out a red marble followed by a blue marble?

Guided Exercise #2 Suppose you are going to draw two cards from a standard deck. What is the probability that the first card is an ace and the second card is a jack? a) With replacement a) Without replacement