Multiplication Rule for Probability

Multiplication

Rule of

Probability

Open Ended

It is time to test your eyes. This test includes a optical illusion showing a old man. However an animal is hidden in this picture. Can you solve this picture brain teaser by finding and naming the hidden animal?

 

​Puppy holding a bone

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

Match

Match the following

• $$A\cup B$$

• $$A'$$

• $$A\cap B'$$

• $$\left(A\cup B\right)'$$

• $$BUC$$

Multiple Choice

Find the P(B).

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

• $$\frac{13}{25}$$

• $$\frac{1}{25}$$

• $$\frac{21}{25}$$

• $$\frac{12}{25}$$

Labeling

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

30

8

6

16

11

5

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?

• $$\frac{4}{5}$$

• $$\frac{3}{5}$$

• $$\frac{1}{5}$$

• $$\frac{3}{20}$$

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

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?

• $$\frac{1}{18}$$

• $$\frac{10}{81}$$

• $$\frac{5}{36}$$

• $$\frac{7}{9}$$

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.

Multiple Choice

Brent has a shopping bag with 8 similar size containers of yogurt: 2 strawberry, 3 cherry, and 3 raspberry. If he randomly takes 2 yogurt containers from the bag without replacement, what is the probability that neither will be strawberry yogurt?

Hint 1 - Probability that the event will occur.

• $$\frac{1}{28}$$

• $$\frac{13}{28}$$

• $$\frac{15}{28}$$

• $$\frac{27}{28}$$

Multiple Choice

Nick randomly selects a digit from the set {0, 1, 2, ..., 9} and a letter from the set {A, B, C, ..., Z}. Matthew will try to guess both the digit and the letter. Which expression gives the probability that Matthew will correctly guess both the digit and the letter?

• $$\frac{1}{10}+\frac{1}{26}$$

• $$\frac{1}{10}\times\frac{1}{26}$$

• $$\frac{9}{10}+\frac{25}{26}$$

• $$\frac{9}{10}\times\frac{25}{26}$$

Multiple Choice

A box contains 7 yellow, 3 red, and 2 white balls. If one ball is drawn from the box, what is the probability of getting a non-yellow ball?

• 5/12

• 7/8

• 7/12

• 5/8

Multiple Choice

There are 4 black marbles and 2 white marbles in a bag, what is the probability of choosing a black marble, not replacing it and then choosing white.

• 8/30 = 4/15

• 3/17

• 6/30 = 1/5

• 8/36 = 2/9

Multiple Choice

You pick two marbles from the bag of 9 marbles. What is the probability you pick both green if you replace the first marble before drawing the second marble?

• 16/81

• 16/9

• 4/27
• 12/72

Multiple Choice

In a standard deck of 52 cards, what is the probability of drawing one ace after another ace on two draws (no replacing)?

• 12/2652 = 1/221

• 1/4

• 16/2704 = 1/169

• 4/52 = 1/13

Multiple Choice

A jar contains 4 white chips, 5 purple chips, and 1 black chip. Chips are selected randomly one at a time, and are not replaced.

What is P(purple then black)?

• 5/90 = 1/18

• 5/100 = 1/20

• 6/90 = 1/15

• 6/100 = 3/50

Lesson Recap