St. James 04-09-20Probability Add Rule, Mult. Rule, Mutual Excl.

🎯 Objectives:

• I can determine if events are independent or dependent.

• I can calculate conditional probability in real-world contexts.

• I can apply geometric models (like area) to calculate probability.

​Take out your notes/graphic organizer

Probability

​***Uniform Sample Space = equal chance for all outcomes***

​ONE Event

Two or more Events

Independent Compound
Events

The events DO NOT affect each other (marbles in a bag)

The item is REPLACED
(Marble is put back in bag)

Dependent Events

The events DO AFFECT each other

The item is NOT REPLACED
(Marble is NOT put back)

Mutually Exclusive

Mutually Exclusive- Two events that have no outcomes in common or
_______________ happen at the same time (there is no overlap in the sample spaces).

Two events are _____ mutually exclusive if they _________ happen at the same time (meaning there is overlap in the sample spaces).

Mutually Exclusive

A.) You randomly select an 8 or a face card from a standard deck of cards.

Not Mutually Exclusive

b.) You randomly select a face card or a diamond from a standard deck of cards.

​Cannot

​NOT

​CAN

​4

​12

​9

​3

​52 cards

​ 8 face Card

​Face Card Diamond

Both (Diamond, Jack, Queen, King)

​10

​A.) You randomly select an 8 or a face card from a standard deck of cards.

Mutually Exclusive

​Can't happen at the same time. No overlap in sample space.

B.) You randomly select a face card or a diamond from a standard deck of cards.

​Not Mutually Exclusive

Can happen at the same time. Overlap in Sample Space.

Fill in the Blanks

Two events are ___________ ___________ when the two events cannot occur at the same time. The events have no outcomes in common.

Multiple Choice

When rolling a single die, the events of rolling an even and an odd number are mutually exclusive.

• True

• False

Categorize

Options (6)

Deck of cards; drawing a 4 or drawing a 6

Deck of cards; Drawing a 4 or drawing a heart

Select a student; a junior or a senior

Select a student; sophomore or a business major

Chef decides; parmesan chicken or grilled sirloin

Roll a die; get an even number or a number < 3.

Organize these options into the right categories

Mutually Exclusive

Not Mutually Exclusive

Multiple Choice

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

• $$\frac{3}{20}$$

• $$\frac{1}{5}$$

• $$\frac{3}{5}$$

• $$\frac{4}{5}$$

Multiple Choice

What is the probability that the person picked will be a boy given they speak german? 

• .7273
• .4
• .16
• .22

Multiple Choice

Find the probability of choosing a card at random that is a spade OR a 7

• 1/52

• 1/13

• 4/13

• 17/52

Multiple Choice

If you draw one card from a standard deck, what is the probability of drawing a 5 or a diamond?

• 2/52

• 4/52

• 4/13

• 26/52

Multiple Choice

If you roll one die, what is the probability of getting an even number or a multiple of 3?

• 1/3
• 2/3
• 1/2
• 1/6

Multiple Choice

What is the probability of choosing a vowel from the alphabet?

• 21/26
• 5/26
• 1/21
• 7/21

Multiple Choice

Event A has a probability of 0.3. What is the probability of the complement of Event A?

• 30%

• 3/100

• 7/100

• 0.7

Multiple Choice

Which of the following shows how to determine P(packers or male)?

• 75/150 + 90/150 - 50/150
• 75/150 + 35/150 - 25/150
• 50/150 + 40/150 + 25/150
• 90/150 + 50/150 - 75/150

Multiple Choice

Which of the following shows how to determine P(skateboard or rollerblades)?

• 48/100 + 42/100 - 39/100
• 39/100 + 3/100 - 49/100
• 49/100 + 9/100 - 3/100
• 9/100 + 3/100 - 39/100

Multiple Choice

If a spinner is numbered 1 – 8, when you spin it the events of spinning an even number and a number less than 4 are mutually exclusive.

• True

• False

Multiple Choice

Is the event INDEPENDENT or DEPENDENT?
The spinner is spun twice.  What is the probability that it lands on red first and then blue?

• Independent
• Dependent

Multiple Choice

Is the event INDEPENDENT or DEPENDENT?

Amy plays card games. She picks a card at random. Then WITHOUT putting the first card back, he picks a second card at random.

• Independent

• Dependent

The Addition Rule

Refresher Probability "OR" so ADD!

​Algebra I Key NB Fall 05-06 part 1.pdf

Multiplication Rule

Upload your completed HW to Canvas

STEPS TO UPLOAD ASSIGNMENT
Take a pic of your assignment
Open your Canvas
Click on Modules
Click on Practical Proportions: Making Sense of Ratios, Precents, and Real-World Math
Click on 03-21-2025 Upload 3-4 Return of Percent's Assignment
Click on Start Assignment
Click on Choose a file to upload
Find the pic of your assignment-- click on the pic--
If there is more than one pic, hold down CTRL and click on all the
pics you need
Click on Submit Assignment

Multiple Choice

Ten cards numbered 1-10 are placed in a hat. What is the probability of randomly drawing a card with an even number then a card with a number greater than or equal to five if the first card is replaced?

• $$\frac{1}{4}$$

• $$\frac{2}{3}$$

• $$\frac{3}{10}$$

• $$\frac{3}{5}$$

Multiple Choice

What is the probability of tossing a coin four times and getting tails each time?

• $$\frac{1}{16}$$

• $$\frac{1}{8}$$

• $$\frac{1}{2}$$

• $$\frac{1}{4}$$

Multiple Choice

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement. P(both marbles are purple) =

• $$\frac{2}{9}$$

• $$\frac{1}{3}$$

• $$\frac{1}{2}$$

• $$\frac{1}{4}$$

Multiple Choice

A coin and a number cube with the numbers 1 through 6 are tossed. What is the probability of the coin showing tails and the number cube showing the number 3? 

• 1/12
• 1/4
• 1/8
• 1/2

Multiple Choice

Two cards are drawn from a standard deck of cards and no cards are returned to the deck. Identify whether the events are independent or dependent. 

• Independent
• Dependent

Poll

What is your level of confidence?