Expected Outcomes Worksheet
Grade 7 Mathematics • Probability & Statistics
Expected Outcomes & Predictions
CCSS 7.SP.C.6 / 7.SP.C.7
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The Core Prediction Formula Expected outcomes = portion or percentage of trials
\(\text{Expected Outcomes} = \text{Probability of Event } P(E) \times \text{Total Number of Trials } (n)\)
Theoretical Probability: Based on math sample space:
\(P(E) = \frac{\text{favorable outcomes}}{\text{total possible outcomes}}\)
Experimental Probability: Based on recorded trial data:
\(P(E) = \frac{\text{favorable outcomes observed}}{\text{total trials recorded}}\)
1 Predictions from Theoretical Probability (Model Examples)
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Example 1:
If the spinner is spun 50 times, how many times can it be expected to stop on 4?
Theoretical \(P(4)\):
\(P(4) =\) fraction or decimal
Expected \(= P(4) \times (\#\text{ trials})\):
Expected = times
J K L M
Example 2:
If the spinner is spun 40 times, how many times can it be expected to stop on J?
Theoretical \(P(\text{J})\):
\(P(\text{J}) =\) fraction or decimal
Expected \(= P(\text{J}) \times (\#\text{ trials})\):
Expected = times
2 Predictions from Experimental Probability (Data-Based)
Example 3:
An experiment was performed. The number 2 occurred 15 times out of 50 trials. Based on this data, how many times can you expect a 2 to occur in 75 trials?
Experimental \(P(2) = \frac{\text{favorable}}{\text{total trials}}\):
\(P(2) =\) simplify fraction
Expected in 75 trials:
Expected = times
Example 4:
Morning Donuts sold 14 donuts, of which 7 were cake donuts. Considering this data, how many of the next 6 donuts sold would you expect to be cake donuts?
Experimental \(P(\text{cake}) = \frac{\text{cake donuts}}{\text{total sold}}\):
\(P(\text{cake}) =\) simplify fraction
Expected in next 6 sales:
Expected = donuts
Unit 3: Expected Outcomes & Probability Predictions Page 1 of 4
Part 2 • Theoretical Probability
Guided Practice: Spinner & Number Cube
\(\text{Expected} = P(\text{Event}) \times \text{Trials}\)
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GP1) Predicting Outcomes on a 6-Section Spinner
Theoretical probability of landing on the number 2: \(P(2) = \frac{1}{6} \approx 0.167\).
Calculate the expected number of times the spinner stops on 2 for each number of spins:
| Number of Trials | Show Multiplication Work: \(P(2) \times (\#\text{ trials})\) | Expected Outcomes |
|---|
| 6 spins | | |
| 12 spins | | |
| 18 spins | | |
| 240 spins | | |
Pattern Check: As the number of trials increases by a factor of 2, what happens to the expected outcomes?
GP2) Number Cube Roll Simulation (42 Trials)
A fair 6-sided number cube (numbered 1 through 6) is rolled 42 times. Calculate the expected occurrences:
a) Land on the number 5?
Expected: times
b) Land on an even number?
Expected: times
c) Land on a 5 or 6?
Expected: times
Extension: How many times would you expect to roll a number less than 3 (1 or 2) in 42 rolls?
Work & Answer:
💡 Conceptual Checkpoint:
If you actually roll a number cube 42 times, are you guaranteed to get exactly the expected number of fives? Explain why or why not in one complete sentence:
Unit 3: Expected Outcomes & Probability Predictions Page 2 of 4
Part 2 • Experimental Probability
Guided Practice: Real-World Data Scenarios
\(\text{Expected} = \frac{\text{favorable}}{\text{trials}} \times \text{new trials}\)
GP3) Abdul's Weighted Coin Experiment
Non-Uniform Coin
Abdul flips a weighted coin 64 times and records 16 tails. Based on experimental probability, how many of the next 40 flips should Abdul expect to come up tails?
Step-by-Step Work:
1. Find experimental \(P(\text{tails}) = \frac{16}{64} =\) ________
2. Multiply by next 40 flips: ________ \(\times 40 =\)
Expected Tails
tails
*Question: Why can't Abdul assume the probability of tails is \(\frac{1}{2}\) for this coin?
GP4) Grocery Store Soup Inventory
Sales Trends
A grocery store recently sold 12 cans of soup, of which 6 were black bean soup. Based on experimental probability, how many of the next 20 cans sold would you expect to be black bean soup?
Step-by-Step Work:
1. Find experimental \(P(\text{black bean}) = \frac{6}{12} =\) ________
2. Multiply by next 20 cans: ________ \(\times 20 =\)
Expected Cans
cans
GP5) Jennifer's Pie Shop Sales Record
Multi-Category Data
| Flavor | Sold |
|---|
| lemon meringue | 2 |
| apple | 3 |
| peach | 2 |
| blueberry | 4 |
| coconut cream | 1 |
| Total Sold | 12 |
a) Considering this data, how many of the next 15 pies sold should you expect to be blueberry pies?
Expected Blueberry: pies
b) How many of the next 24 pies sold would you expect to be apple pies?
Expected Apple: pies
Key Takeaway: In experimental probability, always find the simplified ratio from past records before multiplying by the new trial amount.
Unit 3: Expected Outcomes & Probability Predictions Page 3 of 4
Part 3 • Mastery Check
Independent Practice & Exit Ticket
Apply Theoretical & Experimental Methods
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- Expected stops on number 2 (\(P(2) = \frac{1}{5} = 0.20\)):
5 spins
10 spins
35 spins
250 spins
- Sweet Treats Bakery
Croissants8
Brownies2
Cake5
Considering this data (total 15), how many of the next 18 desserts sold should be slices of cake?
Expected: slices
- Joe's Soccer Shots
Joe scored a goal on 8 out of his last 32 shots.
How many goals would you expect Joe to score on his next 12 shots?
Hint: \(P(\text{goal}) = \frac{8}{32} = \frac{1}{4}\)
Expected: goals
- Sock Drawer
Mark randomly draws a sock 100 times, replacing it after each pick.
| Color | Count |
|---|
| Blue | 5 |
| White | 7 |
| Gray | 8 |
A. Total socks:
B. How many times can Mark expect to pull a gray sock in 100 trials?
Expected Gray Socks = times
C. Reasoning: Why is it mathematically essential that Mark replaces the sock after each pick?
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- Unequal Sector Spinner (Total = 60 Spins)
Notice sector sizes: Sector 2 is \(\frac{1}{2}\); Sector 3 is \(\frac{1}{4}\); Sector 4 is \(\frac{1}{4}\). The spinner is spun 60 times:
a) Land on 3?
times
b) Land on 2?
times
c) Number > 2?
times
🎟️ Exit Ticket: Lesson 3 Check Score: ____ / 4
1. A 6-sided die is rolled 60 times. How many times would you expect an odd number?
2. In 20 free throws, Maya made 14. How many makes would you expect in her next 50 shots?
Unit 3: Expected Outcomes & Probability Predictions Page 4 of 4
