Probability Notes

Probability Study Guide

By Kimberlee Joy

Experimental vs. Theoretical

​Experimental: Theoretical:

​

P(Heads) = 13/20 P(Heads) = 1/2

P(Tails) = 7/20 P(Tails) = 1/2​

Multiple Choice

On this spinner, what is P(A)?

• ³/₈

• ⁴/₈

• ²/₈

• ⁵/₈

Multiple Choice

On this spinner, what is P(not A)?

• ³/₈

• ⁴/₈

• ²/₈

• ⁵/₈

Multiple Choice

You completed an experiment where you rolled a dice 12 times and recorded your data in the table above. What is the experimental probability of rolling a 4?

• 2/6

• 1/6

• 1/12

• 5/12

Multiple Choice

If a counter is selected at random from this bag, what is P(yellow)?

• ²/₃

• ²/₅

• ³/₅

• ¹/₅

Multiple Choice

The chart below represents the number of marbles in a jar.
P(green) = 

• 5/19
• 10/28
• 5/14

Multiple Choice

You completed an experiment where you rolled a dice 12 times and recorded your data in the table above. What is the experimental probability of rolling an odd number?

• 5/12

• 1/12

• 7/12

• 11/12

Fill in the Blank

A counter is picked at random from the bag

Find: P(White)

Give answer as a fraction.

Fill in the Blank

A fair six-sided dice is rolled

Find: P(More than 2)

Give answer as a fraction.

Multiple Choice

Rylee is on a weekend fishing trip with her family. So far she has caught 4 trout, 10 catfish, and 13 bluegill. What is the probability that the next fish that Rylee catches will be a catfish?

• 37%

• 15%

• 48%

• 38%

Fill in the Blank

10 cards are numbered 1-10

One card is picked at random

Find: P(Multiple of 3)

Give answer as a decimal

Making Predictions: Probability times total amount

Using the data above, how many times would you expect the #5 to be picked out of a total frequency of 100 times

(round to nearest whole #)​

​

7/30 x 100 = about 23 times​​

​

Fill in the Blank

Predict how many times someone would land on a number less than or equal to 5 if they rolled a die 90 times

Multiple Choice

100 second graders were asked to do a book report about one of these four zoo animals.  The number of students who chose each animal is shown in the table.  If 250 second graders had to choose of of the four animals, predict how many would choose to write about a giraffe.

• 60 students
• 50 students
• 40 students
• 30 students

Multiple Choice

150 people were polled on their favorite sport.  Based on the table, if you asked only 25 people what their favorite sport is, how many would say soccer is their favorite sport?

• 5 people
• 6 people
• 8 people
• 10 people

"OR"

add

Be careful to subtract out any OVERLAPS

Multiple Choice

On this spinner, what is P(D or E)?

• ¹/₈

• ³/₄

• ¹/₄

• ⁷/₈

Multiple Choice

A jar contains 2 pink, 6 red, and 4 blue marbles. If you pick one marble without looking, what is the probability that the marble you pick will be red or blue?

• 5/6
• 1/2
• 1/3
• 1/6

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

Fill in the Blank

10 cards are numbered 1-10

One card is picked at random

Find: P(Even number or 7)

Give answer as a decimal

Multiple Choice

Which of the following shows how to determine P(shaded number or number less than five)?

• 4/8 + 4/8 - 2/8
• 4/9 + 2/8 - 4/8
• 4/8 + 6/8 + 2/8
• 2/8 + 4/8 - 4/8

Multiple Choice

A pair of dice are rolled, find the probability that the sum is equal to 4 or doubles

• $$\frac{1}{4}$$  

• $$\frac{2}{9}$$  

• $$\frac{5}{18}$$  

• $$\frac{1}{72}$$  

"AND"

multiply

​COMPOUND more than one event

Multiple Choice

You roll two die.

What is the probability you will roll a 4, then roll a number less than 3?

• 1/36

• 1/18

• 1/9

• 1/6

Multiple Choice

What is the probability of flipping a coin

3 times and getting 3 heads?

• 1/8

• 1/4

• 1/2

• 3/4

Multiple Choice

What is the probability of rolling an even number and spinning green?

• 1/8

• 1/15

• 4/8

• 1/10

Multiple Choice

You are fishing in a small pond containing 7 bass, 4 sunfish, 6 catfish, and 3 goldfish.  If you throw the fish back after each catch, what is P(bass, then goldfish)?

• $$\frac{1}{20}\cdot\frac{1}{20}=\frac{1}{400}$$

• $$\frac{7}{20}+\frac{3}{20}=\frac{11}{20}$$

• $$\frac{7}{20}\cdot\frac{3}{20}=\frac{21}{400}$$

• $$\frac{7}{20}\cdot\frac{3}{19}=\frac{21}{380}$$

Two-Way Tables

BEWARE OF OVERLAPS

Multiple Choice

What is the probability of someone traveling in First or Second Class?

• 610/2201

• 321/2201

• 289/2201

• 325/2201

Multiple Choice

According to the table, what is

P(student 10-13 OR skip breakfast)

• $$\frac{9}{50}$$  

• $$\frac{83}{90}$$  

• $$\frac{7}{27}$$  

• $$\frac{97}{90}$$  

Multiple Choice

What is the probability that someone has black or brown eyes?

• 90/167

• 45/45

• 2025/4489

• 45/167

Multiple Choice

What is the P(Boy or can't bike)?

• $$\frac{7}{10}$$  

• $$\frac{5}{6}$$  

• $$\frac{4}{11}$$  

• $$\frac{2}{15}$$  

Multiple Choice

The Bargain Auto Mall has these cars in stock.  If a car is selected at random, find the probability that it is Foreign and mid-sized.

• 20/300
• 135/300
• 155/300
• 40/300

Multiple Choice

What is P(male or SUV)?

• $$\frac{7}{20}$$  

• $$\frac{7}{80}$$  

• $$\frac{13}{16}$$  

• $$\frac{9}{10}$$  

Multiple Choice

What is the probability that someone lived and was working on the Crew?

• 212/2201

• 212/711

• 212/885

• 711/2201

"Given" situations

​Denominator is not grand total anymore!

Multiple Choice

Given that someone survived, what is the probability that they were traveling in First Class?

• 711/203

• 203/711

• 203/2201

• 711/2201

Multiple Choice

What is the probability that someone died given that they were traveling Third Class?

• 528/706

• 706/2201

• 528/2201

• 706/528

Multiple Choice

What is the probability that they speak French given they are a girl? 

• 2.14
• .24
• .4
• .8571

Multiple Choice

Given that someone has green eyes, what is probability that person is male?

• 20/35

• 15/35

• 35/167

• 82/167

Multiple Choice

What is the probability that a student does play a sport given they do not play an instrument? 

• .2
• .2222
• .10
• .5