7th Grade Probability and Probability Models Worksheet Solutions (PDF)
This probability models answers for 7th Grade covers probability and probability models (Common Core 7.SP.C.5, 7.SP.C.6, 7.SP.C.7), with a free PDF to print.
Use this answer key to check your work on the probability models worksheet. Every solution shows the steps, and the final answer appears in bold. If your answer is different, compare each step and look for the first place where the work changes.
Grade 7 · Common Core State Standards: 7.SP.C.5, 7.SP.C.6, 7.SP.C.7
Probability models answers: exercises 1 to 10
Exercise 1 – Impossible event
No face shows 7, so there are 0 favorable outcomes.
\(P=0\div 6=0\)
0; impossible
Exercise 2 – One outcome
1 favorable outcome out of 6.
\(\frac{1}{6}\)
Exercise 3 – Even number
Even faces: 2, 4, 6, which is 3 outcomes out of 6.
\(\frac{3}{6}=\frac{1}{2}\)
\(\frac{1}{2}\)
Exercise 4 – Prime number
Primes: 2, 3, 5, which is 3 outcomes of 6.
\(\frac{3}{6}=\frac{1}{2}\)
\(\frac{1}{2}\)
Exercise 5 – Marble bag
Total: \(5+3+2=10\).
\(P(\text{red})=\frac{5}{10}=\frac{1}{2}\).
\(P(\text{not red})=1-\frac{1}{2}=\frac{1}{2}\)
\(\frac{1}{2}\) and \(\frac{1}{2}\)
Exercise 6 – Spinner
\(\frac{3}{8}\)
\(\frac{3}{8}\)
Exercise 7 – Letter cards
Vowels: A, E, A, I, which is 4 cards out of 11.
\(\frac{4}{11}\)
Exercise 8 – Relative frequency
\(\frac{38}{60}=\frac{19}{30}\approx 0.63\).
The theoretical probability is 0.5; with 60 tosses a difference is expected.
\(\frac{19}{30}\approx 0.63\)
Exercise 9 – Predict rainy days
\(0.35\times 20=7\)
About 7 days
Exercise 10 – Spin results
\(\frac{18}{50}=0.36\), \(\frac{12}{50}=0.24\), \(\frac{20}{50}=0.40\).
Check: \(0.36+0.24+0.40=1\)
0.36, 0.24, 0.40
Exercises 11 and up
Exercise 11 – Missing probability
The probabilities add up to 1.
\(1-0.4-0.3=0.3\)
0.3
Exercise 12 – Expected rolls
\(\frac{1}{6}\times 120=20\)
About 20 times
Exercise 13 – Complement
\(1-0.35=0.65\)
0.65
Exercise 14 – Probability model
Common denominator 12: \(\frac{2}{12}+\frac{3}{12}+\frac{4}{12}=\frac{9}{12}\).
\(x=1-\frac{9}{12}=\frac{3}{12}=\frac{1}{4}\)
\(\frac{1}{4}\)
Exercise 15 – Snow days
\(0.15\times 60=9\)
About 9 days; unlikely on any given day
Exercise 16 – Free throws
\(\frac{36}{48}=\frac{3}{4}\).
\(\frac{3}{4}\times 20=15\)
About 15
Exercise 17 – Raffle
\(\frac{4}{200}=\frac{1}{50}=0.02=2\%\)
\(\frac{1}{50}\), or 2%
Exercise 18 – Lunch choice
Relative frequency: \(\frac{14}{40} = 0.35\).
\(0.35 \times 100 = 35\)
About 35 greens
Exercise 19 – Die experiment
\(\frac{9}{40}=0.225\) compared with \(\frac{1}{6}\approx 0.167\).
The experiment gave 5 more often than the theory predicts, which can happen by chance.
\(\frac{9}{40}=0.225\) versus \(\frac{1}{6}\approx 0.167\)
Exercise 20 – Adding marbles
New total: \(10+2=12\). Red: \(5+2=7\).
\(P(\text{red})=\frac{7}{12}\approx 0.58\), which is greater than \(\frac{1}{2}\).
\(\frac{7}{12}\), greater than before
Key facts behind this probability models answers
- Probability is between 0 (impossible) and 1 (certain).
- Equally likely outcomes: \(P = favorable \div total\).
- Relative frequency = number of times the outcome happens ÷ number of trials.
- The probabilities of all outcomes in a model add up to 1.
- \(P(not A) = 1 – P(A)\).
How to use this probability models answers
Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.
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