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This Probability Packet Belongs to: __________________________________

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Station #1: M & M’s

1. What is the sample space of your bag of M&M’s?

2. Find the theoretical probability of the M&M’s in your bag. Then, place the candy back

into the bag, pull out an M&M and record the results under experimental probability.

Repeat for a total of 20 times.

Theoretical Probability Experimental Probability

Candy

Color

Total # of

each color

in bag

Color

Total

% color in

your bag

Tally

Marks- 20

times

Color Picked

20 tries %

Red

Blue

Yellow

Green

Brown

Orange

3. Is the experimental probability of the colors you picked in the 20 tries equal to the

theoretical probability found in the bag? Why or why not?

4. P(choosing a yellow without replacing it & then a blue)

5. P(choosing a yellow or a brown)

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Station #2: Money Toss

1. Take 2 coins, a penny and a nickel, and predict all the possible outcomes that can

occur when you toss the 2 coins. Record your results in the table below. Find the theoretical

probability for each outcome.

Theoretical Probability

Outcome

Penny Nickel Fraction Percent

1

2

3

4

1. Toss both coins 20 times and record your results in the table below. (Tails/ Heads)

Event Penny Nickel Event Penny Nickel

1 11

2 12

3 13

4 14

5 15

6 16

7 17

8 18

9 19

10 20

2. Use the information in # 1 & #2 above to complete the table below.

Theoretical Probability Experimental Probability

Event Fraction Percent Fraction Percent

Both coins are

heads

At least one

coin falls tails

One head and

one tail

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3. Write a complete sentence comparing the experimental probability and the

theoretical probability.

Station #3: M & M’s in a Bag

Using the M & M clue cards on the website agenda, determine how many colors of each

M & Ms there are in the bag.

Brown: _________________________

Blue: _________________________

Green: _________________________

Orange: _________________________

Yellow: _________________________

Station #4: Draw the Spinner

Using the spinner clues on the website agenda, draw what the spinner would look like. Draw

spinner 1 first and then draw spinner 2.

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Station #5: Deck of Cards: Ace (1), 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack (11), Queen (12), King (13)

Clubs: Diamonds: Spades: Hearts:

1. Take a standard deck of cards containing 52 cards and determine the theoretical

probability of picking the following cards.

Theoretical Probability

Event Fraction Percent Event Fraction Percent Ace of

Spades

A Heart or a

Diamond

A Numbered

Card

An Ace or a

King

A Red

Card Not a Club

A Queen A Seven, Eight or

Nine

A Red or

Black Card Not a Face Card

Jack of Hearts Queen of

Diamonds

Not a Red or

Black Card

A Two, Three,

Four or Five

Two of Clubs A Prime

Numbered Card

2. Randomly, pick a card 20 times (replacing the card each time) and record your

results. This is your experimental data. Use initials for your data (ie. KS is King of

Spades). Spades (S), Clubs (C), Hearts (H), Diamonds (D)

Event Card Event Card Event Card Event Card

1 6 11 16

2 7 12 17

3 8 13 18

4 9 14 19

5 10 15 20

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3. Experimental Probability- Record your results from page 6 in the chart below.

Event Fraction Percent Event Fraction Percent

Ace of

Spades

A Heart or a

Diamond

A Numbered

Card

An Ace or a

King

A Red

Card

Not a Club

A Queen A Seven, Eight or

Nine

A Red or

Black Card Not a Face Card

Jack of Hearts Queen of

Diamonds

Not a Red or

Black Card

A Two, Three,

Four or Five

Two of Clubs A Prime

Numbered Card

4. Compare the theoretical results with the experimental results from the two charts

above. Explain your findings.

Station #6: Spinners- Use the spinner link on the website agenda.

Spinner #1: This spinner has 3 red, 3 blue, and 2 green regions.

1. Spin the spinner 10 times and record your results below.

Event Color Event Color

1 6

2 7

3 8

4 9

5 10

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2. The pointer is equally likely to stop on any of the spaces. Find the theoretical

probability (TP) and experimental probability (EP) from the above data of each of the

following:

Event Theoretical Experimental

Fraction % Fraction %

a blue region

a green region

a red region

a non-blue region

a non-green region

Spinner #2: This spinner has 4 brown, 2 yellow, 3 purple, and 3 orange spaces.

3. Spin the spinner 10 times and record your results.

Event Color Event Color

1 6

2 7

3 8

4 9

5 10

4. Find the theoretical probability (TP) and experimental probability (EP) from the above

data of each of the following:

Event Theoretical (TP) Experimental (EP)

Fraction % Fraction %

a brown region

a purple region

a yellow or orange region

a non-yellow region

a non-purple region

5. Write a complete sentence comparing the experimental probability and the theoretical

probability.

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Station #7: Dice Toss

1. The list shown lists all the possibilities when rolling 2 six-sided number cubes.

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

2. How many different possibilities are there when rolling 2 six-sided number cubes?

3. Complete the addition chart. List all of the theoretical probabilities that can occur

when rolling two dice and record below.

+ 1 2 3 4 5 6

1

2

3

4

5

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4. Using the chart above, write the theoretical probability as a fraction and then as a

percent for each number.

Probability Fraction Percent Probability Fraction Percent

P(1)

P(7)

P(2) P(8)

P(3) P(9)

P(4) P(10)

P(5) P(11)

P(6) P(12)

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5. Is there an equally likely chance for each number to result from rolling 2 six-sided

number cubes according to the theoretical probabilities?

6. If the number cubes are tossed 180 times, how many times do you predict the

following sums would occur?

Outcome Theoretical Probability Prediction /180

1

4

9

Prime Number

Composite Number

7. Throw a pair of dice 50 times. Add the two dice and record with tally marks below to

find the experimental probability. Then find the fraction & percent out of the 50 rolls.

Sum # of rolls Fraction Percent Sum # of rolls Fraction Percent

1

7

2

8

3

9

4

10

5

11

6

12

Which sum is impossible? ________________________________

Which sum occurs most often? ____________________________

Which sum occurs least often? ____________________________

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8. Make a line plot for the theoretical & experimental probability of the sum outcomes of

the dice rolls. Make a key & assign a different color to the theoretical & experimental

results.

9. How does the experimental probability compare to the theoretical probability?

Explain your findings.

Station #8: Probability and Your Class

Jarek Sophie Felipe Justice Leo Lexxie

Zach Paige Jenna Olivia Mano Hailey

Sean Stephanie Darin Keira Luke Maddie

Andrea Pablo Jack Cassie Michael Alex

Use the class list to determine the probabilities of the following events. Suppose that each of

these names were written on a card and the cards were shuffled and kept facedown. What

are the chances of drawing classmates name with?

1.) The first letter being D?______________

2.) A five letter name? ______________

3.) A name in which the first letter is a vowel?______________

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4.) Double letters that are adjacent? (Ex. Annie) ______________

5.) The letter “a” somewhere in their name?______________

6.) A name that contains more than 4 vowels?______________

7.) A name that contains three or more syllables? ______________

8.) A name that has the total number of letters equaling a prime number? ______________

9.) A name that begins and ends with the same letter? ______________

10.) A name with seven or more letters? ______________

11.) How many total letters do you think there are in all the names?

Estimate: ______________Actual: ______________

12.) What is the probability that a girl will be chosen first, not replaced and another girl will be

chosen? Show your work.

13.) What is the probability that a girl will be chosen first, replaced and a boy will be chosen

second? Show your work.

14.) What is the probability that a girl will be chosen first, not replaced and then a boy will be

chosen? Show your work.

15.) What is the probability that a person’s name starting with a vowel will be chosen, not

replaced and then another person’s name starting with a vowel will be chosen? Show your

work.

16.) What is the probability that a name starting with the letter A will be chosen, replaced,

and then the letter T? Show your work.

17.) What is the probability that a name starting with the letter M will be chosen, not

replaced and another M will be chosen? Show your work.

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Station #9: Rock, Paper, Scissors

1. What is the theoretical probability of getting rock, paper, and scissors?

_______________ _______________ _______________

2. With a partner, play this game 30 times and fill out the table to record the results that

represent experimental probability. Each time you make a move, record which

outcome you made. If the outcome was a win, write a tally in the wins category for

rock, paper, scissors that made the win.

Circle which player # you represent. Keep track in your own packet.

Player #1 #2

Result Tallies/

30

Number of Wins Total Outcomes as

a Fraction Percentage

3. How did the theoretical probability & the experimental probability compare?

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Station #10: Tossing Cups

1. Find the theoretical probability of the tossing the cup and it landing on its end and

side.

Station #10: Tossing Cups

Cup Landing Position Theoretical

Probability Fraction Percent

End

Side

2. The game is played between two players. To play the game, cup is tossed in the air. Play the

game 25 times with a partner. Decide who will be Player 1 and who will be Player 2. Record

your results in the table using tally marks. Then, write your and your opponent’s total score, and

write the number of times the cup landed on its side. Calculate the fraction, percent and total

points.

Tossing Paper Cups

Experimental Probability Cup Landing Position Tallies / 25 Fraction Percent Total Points

Player #1

Side

Player #2

3. Do you think this is a fair game to play? Why or why not?

4. When you toss a six-sided number cube, the probability of it landing on any of the

numbers from 1 through 6 is 1

6. Is it possible to determine the exact probability of the

cup landing on its top, bottom, or side? Explain your reasoning.

End

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Points