7th Grade Math
Name:________________________________________
Probability Stations
Color:________________ Date:___________________
Station 1: Spinning a Spinner and Flipping a Coin
1. Is this an independent or dependent event?_______________________
2. Spin the spinner and then flip the coin. Record the results in the table below.
3. Repeat step 2 for a total of 20 trials.
Trial #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Spinner
Coin
4. What was the experimental probability of spinning green and getting heads?
5. What is the theoretical probability of spinning green and getting heads?
6. What is the experimental probability of spinning yellow and getting tails?
7. What is the theoretical probability of spinning yellow and getting tails?
8. Based on your experiment, how many times would you get red and heads if you did
50 trials?
9. Based on the theoretical probability, how many times would you get red and heads if
you did 50 trials?
20
Station 2: Scratch Ticket
A fast food chain is running a competition. Customers receive a scratch card with 12
circles on it, each containing either a palm tree or a crab underneath. You can scratch off up to
four circles, and you win if 3 or more palm trees are revealed, but loose if you get two or more
crabs. The card pictured here has all of the circles scratched off.
1. What is ratio palm trees: crabs? What is the ratio
of palm trees: total circles? What is the ratio of
crabs: total circles?
2. Imagine that all the circles are covered up. On the
first scratch, what is the probability of getting
a. a Palm Tree?
b. a Crab?
3. Yay! We got a palm tree on the first scratch! Now we go for the second scratch. What
is the probability of getting
a. a Palm Tree?
b. a Crab?
4. Palm tree again! We only need one more palm tree to win. On the third scratch, what
is the probability of getting
a. a Palm Tree?
b. a Crab?
5. Aw man! We got a crab this time. That’s ok! We still have one more scratch. What will
our probably be of winning on the last scratch?
6. What was our overall probability of getting this particular sequence (PPCP) from the
beginning?
7. The tree diagram below shows the outcomes possible from playing this game
(assuming that you stop scratching once you win/lose). Circle the outcomes that
result in a win and put a box around the ones that result in a loss.
1st scratch
b. What is the probability of winning?
2nd scratch
3rd scratch
4th scratch
a. How many total outcomes are there?
c. What is the probability of losing?
Station 3: M&Ms
I. Replacement: Without looking, reach into the bag and remove an M&M. Record its color
(Brown, Yellow, Red, Orange, Green, Blue) in the slot for trial 1, color 1. REPLACE the M&M
and draw another, recording its color in trial 1, color 2 and replacing it. Repeat the process 15
times.
Trial
Color
1
Color
2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1. Based on your results, calculate the following EXPERIMENTAL probabilities:
(Remember, you drew 30 M&Ms total)
a. P(Br): __________
d. P(O): ___________
b. P(Y): __________
e. P(G): ___________
c. P(R) : __________
f. P(Bl) : _____________
2. Based on your results, calculate the following EXPERIMENTAL probabilities:
(Remember, you did 15 trials)
a. P(O, Bl) = ___________
c. P(O, R) = _________
b. P(Br, Br) = ___________
d. P(Y, Y) = _________
e. Are these events independent or dependent?
II. Without Replacement: Reach into the bag & remove an M&M. Record its color in the trial 1
column. Hold this M&M in your hand & draw a second; record its color in the trial 1 column.
Now REPLACE BOTH M&M’s. Repeat 15 times.
Trial
Color
1
Color
2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
3. Based on your results, calculate the following EXPERIMENTAL probabilities:
(Remember, you did 15 trials)
a. P(O, Bl) = ___________
c. P(O, R) = _________
b. P(Br, Br) = ___________
d. P(Y, Y) = ________
e. Are these events independent or dependent?
15
III. Theoretical Probability: Now count the M&M’s from your bag and record the totals below.
Brown
Yellow
Red
Orange
Green
Blue
TOTAL
4. Draw One: Use the table to calculate the following theoretical probabilities
a.
P(Br): __________
d. P(O): ___________
b. P(Y): __________
e. P(G): ___________
c. P(R) : __________
f. P(Bl) : _____________
** Compare your answers to those in Question 1
5. Replacement: Use the above table to calculate the following theoretical probabilities
when sampling occurs WITH REPLACEMENT
a. P(O, Bl) = ___________
c. P(O, R) = _________
b. P(Br, Br) = ___________
d. P(Y, Y) = _________
** Compare your answers to those in Question 2
6) Without Replacement: Use the above table to calculate the following theoretical probabilities
when sampling occurs WITHOUT REPLACEMENT
a. P(O, Bl) = ___________
c. P(O, R) = _________
b. P(Br, Br) = ___________
d. P(Y, Y) = _________
** Compare your answers to those in Question 3
Station 4: Intransitive Dice
In this dice game, you will play with a partner to try to win the most points. However,
these aren’t regular dice. Each dice has three different numbers on it, repeated twice. Take a
look at them for yourself.
Decide who is player 1 and who is player 2. Player 1 will chose a color to roll, then
player 2 will chose from the two colors that are left. Each player rolls a die and the player with
the higher number wins a point. Record each players color and number in the table below, as
shown in the Example column. Repeat for 20 trials. Whichever player has the highest point total
wins the game!
Trial Ex 1
2
3
4
5
6
7
8
9 10 11 12 13
Player
G6
1
Player
R2
2
**G6 means green dice rolled a 6, R2 means red dice rolled a 2
14
15
16
17
18
19
20
Now we are going to look at the probability involved and see if there is any strategy that we can use to
give us a higher chance of winning the game.
1. Look at all the times the Red dice and the Green dice were rolled together.
What is the experimental probability of Green winning?___________ Of Red winning?____________
2. Look at all the times the Red dice and the Blue dice were rolled together.
What is the experimental probability of Blue winning?___________ Of Red winning?____________
3. Look at all the times the Blue dice and the Green dice were rolled together.
What is the experimental probability of Green winning?___________ Of Blue winning?___________
4. What patterns do you notice? In each pairing, is there one dice that seems to do better? Is there
one dice that seems better overall?
5. Make some tree diagrams to explain why this is (complete on back of this page)
6. How would knowing this help you increase your chances of winning? Is there a strategy you
would employ? Would you want to be Player 1 or Player 2? Why?
Tree Diagrams (Question 5)
a. Fill in the tree diagram for Red vs. Green and find the theoretical probability of red winning.
Red
Green
1
2
b. Use the model above to make your own tree diagrams for Blue vs. Red and determine
the theoretical probability of Blue winning.
c.
Make a tree diagram for Green vs. Blue and determine the probability of Green
winning.
d. Go back and answer question 6 on the front of this page.
Station 5: Pick a Card, Any Card
At this station, you will investigate probabilities involved in drawing cards from a standard
deck. A standard deck of cards contains

52 cards

4 suits: Diamond (Red)

Each suit has one of each of the following: A, 2-10, J, Q, K, meaning each suit has 13 cards
, Hearts (Red)
, Spades (Black)
, and Clubs (Back)
1. Have one partner fan out the deck of cards. The other partner pulls one card, records its
value and suit, and then sets it aside. They then pull a second card, record its value and
suit, and replace both cards.
2. Switch partners, so now the first partner is picking the cards. Repeat this process until
you have recorded 18 trials.
Trial
Card
1
Card
2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
3. Calculate the experimental probability of pulling two cards of the same value (ex, two
aces, or two 7s etc).
4. Now calculate the theoretical probability of pulling two cards of the same value. (Hint:
does it matter what we pull for the first card? How will our first card affect the probability
of getting a second card of the same value?)
5. Calculate the experimental probability of pulling two cards of the same suit.
6. Now calculate the theoretical probability of pulling two cards of the same value.
7. What is the theoretical probability of pulling three red cards (without replacement)?
8. Let’s calculate the theoretical probability of getting a flush, which is five cards of the
same suit.
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