Addition and Multiplication Rule of Probability

Multiplication

Rule of

Probability

Match

Match the following

• $$A\cup B$$

• $$A'$$

• $$A\cap B'$$

• $$\left(A\cup B\right)'$$

• $$BUC$$

Let's check for understanding from this week's topics.

Multiple Choice

Find the P(B).

Note: $$P\left(Event\right)=\frac{num\ outcomes}{total}$$

• $$\frac{13}{25}$$

• $$\frac{1}{25}$$

• $$\frac{21}{25}$$

• $$\frac{12}{25}$$

Labelling

A guidance counselor is planning schedules for 30 students.  16 want to take Spanish and 11 want to take Latin.  5 Say they want to take both.  Display this information on the Venn diagram.

Drag labels to their correct position on the image

5

16

8

30

11

6

Multiple Choice

Amanda spins a spinner numbered 1 to 10. What is the probability that the spinner lands on an odd number or a number that is divisible by 3?

• $$\frac{4}{5}$$

• $$\frac{3}{5}$$

• $$\frac{1}{5}$$

• $$\frac{3}{20}$$

Multiple Choice

A total of 540 customers, who frequented an ice cream shop, responded to a survey asking if they preferred chocolate or vanilla ice cream.

308 of the customers preferred chocolate ice cream.

263 of the customers were female.

152 of the customers were males who preferred vanilla ice cream.

What is the probability that a customer chosen at random is a male or prefers vanilla ice cream?

• $$\frac{419}{540}$$

• $$\frac{119}{180}$$

• $$\frac{197}{540}$$

• $$\frac{38}{135}$$

Learning
Target

• Students will learn how to utilize

the multiplication rule to
calculate probabilities of when a
second event is impacted by
what happens during the first
event

​

Calculating Probabilities

WHEN WE CALCULATE PROBABILITIES INVOLVING
ONE EVENT AND ANOTHER EVENT OCCURRING,

WE MULTIPLY THEIR PROBABILITIES.

IN SOME CASES, THE FIRST EVENT HAPPENING

IMPACTS THE PROBABILITY OF THE SECOND
EVENT. WE CALL THESE DEPENDENT EVENTS.

IN OTHER CASES, THE FIRST EVENT HAPPENING

DOES NOT IMPACT THE PROBABILITY OF THE
SECONDS. WE CALL THESE INDEPENDENT

EVENTS.

We can represent this
concept with a tree
diagram like the one
shown.

We multiply the
probabilities along
the branches to
find the overall
probability of one
event AND the
next even
occurring.

For example, the probability of
getting two "tails" in a row would be:

When two events are independent,
we can say that

Be careful! This formula only applies
to independent events.

Multiple Choice

A key ring has 12 keys, 3 of which open the house door. If two keys are randomly selected without replacement, what is the probability that neither key opens the door?

• $$\frac{1}{22}$$

• $$\frac{6}{11}$$

• $$\frac{9}{16}$$

• $$\frac{21}{22}$$

Multiple Choice

There are 9 movies showing at a theater. Two are action movies, two are children’s movies, and the other movies are comedies. Ashley randomly selects 2 different movies to see. What is the probability that the first movie is an action movie and the second movie is a comedy?

• $$\frac{1}{18}$$

• $$\frac{10}{81}$$

• $$\frac{5}{36}$$

• $$\frac{7}{9}$$

Note: P(B) = 1 – P(B’)

What is the probability of pulling a King and Queen out of a standard
deck of playing cards? Note: The cards are not replaced once one is
pulled out of the deck.

Lesson Recap