Unit 1 Probability Review

Unit 1: Probability Review

​Sample Space

The sample space is a list of all the possible outcomes of a random experiment.

​​

​

​

​ex. The sample space of flipping a coin is:

• Heads

• Tails​

Multiple Choice

What is the sample space when rolling a 6 sided die?

• 1

• 2, 4, 6

• 1, 2, 3, 4, 5, 6

• 6

Multiple Choice

What is the sample space when choosing one month out of the year?

• Jan., Feb., Mar., April, May, June, July, Aug, Sept, Oct., Nov., Dec.

• Jan., Mar., April, May, June, July, Sept, Oct., Nov., Dec.

• 365 days

• 52 weeks

​Probability - the chance that something will occur.

Math 7 | Probability

​

​Examples:

​What is the probability of the spinner landing on orange?

​What is the probability of the spinner landing on blue?

Probability Number Line

Multiple Choice

Which of the following probabilities is unlikely?

• .30

• .45

• .19

• All of the above.

Multiple Choice

Which statement is true?

• A LIKELY probability is anything over 50%.

• 100% written in decimal form is 10.

• .72 is unlikely since it is less than 1.

• Sample space is always 100.

Simple Probability

Multiple Choice

What is the probability of landing on the color blue on the spinner?

• $$\frac{3}{3}$$

• $$1$$

• $$\frac{3}{12}\ or\ \frac{1}{4}$$

• $$\frac{3}{9}\ or\ \frac{1}{3}$$

Multiple Choice

A die is rolled once.  What is the probability of rolling a 5? Your answer should be a fraction in simplest form.

• $$\frac{1}{6}$$

• $$\frac{1}{3}$$

• $$\frac{2}{5}$$

• $$\frac{5}{6}$$

Multiple Choice

What is the probability of the spinner landing on red?

• $$\frac{5}{12}$$

• $$\frac{7}{12}$$

• $$\frac{5}{5}$$

• $$\frac{5}{10}\ or\ \frac{1}{2}$$

Multiple Choice

A bag has 3 red marbles, 2 blue and 4 green and 1 yellow. What is the theoretical probability of pulling a red?

• $$\frac{3}{10}$$

• $$\frac{3}{9}$$

• $$\frac{1}{10}$$

• $$\frac{1}{9}$$

Venn Diagrams

Multiple Choice

Which notation represents the shaded region?

• $$P\left(A\ ∩\ B\right)$$

• $$P\left(A\ ∪\ B\right)$$

• $$P\left(A\right)$$

• $$P\left(B\right)$$

Multiple Choice

Which notation represents the shaded region?

• $$P\left(A\cup B\right)$$

• $$P\left(A\cap B\right)$$

• $$P\left(A\right)$$

• $$P(B)$$

Complement

Multiple Choice

Which notation represents the shaded region?

• $$P\left(A\right)$$

• $$P\left(B\right)$$

• $$P\left(A^c\right)$$

• $$P\left(B^c\right)$$

Multiple Choice

Which notation represents the shaded region?

• $$P\left(A\cap B\right)$$

• $$P\left(A\cap B^c\right)$$

• $$P\left(B\cap A^c\right)$$

• $$P\left(A\cap B\right)^c$$

Multiple Choice

At Apple Valley High school, there are 150 seniors, 70 own dogs, 30 own cats, and 25 own both. Reduce you answer.
Find

$$P\left(Cat\ \cap Dog\right)$$  

• $$\frac{1}{30}$$  

• $$\frac{1}{6}$$  

• $$\frac{3}{10}$$  

• $$\frac{1}{2}$$  

Multiple Choice

At Apple Valley High school, there are 150 seniors, 70 own dogs, 30 own cats, and 25 own both. Reduce you answer. 
Find

$$P\left(Cat\ \cup Dog\right)$$  

• $$\frac{1}{30}$$  

• $$\frac{1}{6}$$  

• $$\frac{3}{10}$$  

• $$\frac{1}{2}$$  

Multiple Choice

At Apple Valley High school, there are 150 seniors, 70 own dogs, 30 own cats, and 25 own both.  Reduce you answer.
Find

$$P\left(Cat\ \cup Dog\right)^c$$  

• $$\frac{1}{30}$$  

• $$\frac{1}{6}$$  

• $$\frac{3}{10}$$  

• $$\frac{1}{2}$$  

Multiple Choice

What is the sample space?

• 31

• 25

• 6

• 12

Multiple Choice

What is the probability that someone plays basketball AND football $$P\left(B\cap F\right)$$ ?

• $$\frac{9}{31}$$

• $$\frac{12}{31}$$

• $$\frac{4}{31}$$

• $$\frac{15}{31}$$

Multiple Choice

What is the probability that someone does not play basketball $$P\left(B^c\right)$$ ?

• $$\frac{9}{31}$$

• $$\frac{12}{31}$$

• $$\frac{4}{31}$$

• $$\frac{15}{31}$$

Multiple Choice

What is $$P(C\cup W)$$ ?

• .14

• .62

• .82

• .18

Multiple Choice

What is $$P\left(W^c\right)$$ ?

• .80

• .18

• .82

• .62

Mutually Exclusive Events

Events that cannot happen at the same time.
The probability of mutually exclusive events is always zero.

Multiple Choice

Which of the following pairs of events is mutually exclusive?

• Cards: Aces and Spades

• Two dice: Odd and even

• Sit down and stand up

• Sit down and scratch your nose

Drag and Drop

Two events are mutually exclusive if they have​ ​

Placeholder

outcomes in common. The probability of two mutually exclusive events occurring is ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

No

One

Many

1

Between 0 & 1

0

Independent Events

What happens in one event does not change the probability of the
other event happening (Second outcome is not affected by the first
event). Key Word: “with replacement”

For Example: Tossing a coin, rolling dice, picking a card from a deck
with replacement.

Independent Events

Example 1: Landing on Heads after
tossing a coin and rolling a 5 on a
single 6-sided dice.

Example 2: Choosing a 3 from a
deck of cards, replacing it, and then
choosing an ace as the 2nd.

P (A and B) = P(A) ×P(B)

What happens when you toss
the coin does not affect what
happens when you roll the dice.

Event A does not affect Event B
because you replaced the card.

Dependent Events

What happens in the first event affects the outcome of the 2nd event. Key

word “without replacement”

Example 1: Robbing a bank and going to jail.

Example 2: Picking a card from a deck without
replacement. Then, picking another card from the
deck.

PA and B=PA ×P(B given A)

Multiple Choice

If you Flip a coin then roll a 6-sided dice. Is it dependent or Independent?

• Independent

• Dependent

Multiple Choice

Yuki chooses a book from the shelf to read, then Janette chooses a book from the books that remain.

• Independent

• Dependent

Multiple Choice

Kathy draws a 4 from a set of cards numbered 1 - 10, and rolls a 2 on a number cube.

• Independent

• Dependent

• Remember your quiz is tomorrow and will cover the first 3 sections of Unit 1.

• You can use your guided notes on your quiz tomorrow :)