Data Champions

Data Champions Practice Sheet Page 2 of 3

Data Lab: Probability Set Page 3 of 3

07

A game spinner is divided into 8 equal sectors numbered 1 through 8. If the spinner is spun once, what is the probability of spinning a number that is prime OR a multiple of 4?

A) \(\frac{1}{2}\)

B) \(\frac{5}{8}\)

C) \(\frac{3}{4}\)

D) \(\frac{7}{8}\)

Scratch Work:

08

The quality table below shows diagnostic classifications of 100 mobile devices:

Type Defective Functional Total

Laptop34750

Tablet54550

If a device is selected at random, what is the probability that it is a laptop OR is defective?

A) \(\frac{11}{20}\)

B) \(\frac{1}{2}\)

C) \(\frac{3}{5}\)

D) \(\frac{3}{50}\)

Scratch Work:

09

A testing jar contains 5 red diagnostic tokens and 5 blue diagnostic tokens. A student draws a token, records its color, replaces it, and draws a second token. What is the probability that both tokens drawn are red?

A) \(\frac{1}{4}\)

B) \(\frac{2}{9}\)

C) \(\frac{1}{2}\)

D) \(\frac{5}{18}\)

Scratch Work:

10

Given the account distributions of 100 enterprise software clients: Premium accounts (25 Active, 15 Inactive), Basic accounts (35 Active, 25 Inactive). Given that a randomly selected account is Active, what is the probability that it is a Premium account?

A) \(\frac{5}{12}\)

B) \(\frac{5}{8}\)

C) \(\frac{1}{4}\)

D) \(\frac{5}{20}\)

Scratch Work:

Data Champions Practice Sheet Page 3 of 3

Guided Workbook Q8 • Set Unions (Or) Correct Choice: B

Expanse of Core Logic: Apply Set Union Formula: \(N(\text{AWS } \cup \text{ GCP}) = N(\text{AWS}) + N(\text{GCP}) - N(\text{AWS } \cap \text{ GCP})\).
Total certified admins = \(45 + 30 - 15 = 60\).
Probability = \(\frac{60}{80} = \frac{3}{4}\).

Guided Workbook Q9 • Compound Probability Correct Choice: A

Expanse of Core Logic: Dependent events without replacement.
1st Draw: \(P(\text{Defective}) = \frac{2}{10}\).
2nd Draw: \(P(\text{Defective}) = \frac{1}{9}\) (since 1 defective and 1 chip are removed).
\(P(\text{Both Defective}) = \frac{2}{10} \times \frac{1}{9} = \frac{2}{90} = \frac{1}{45}\).

Guided Workbook Q10 • Conditional Probability Correct Choice: C

Expanse of Core Logic: Given that the candidate passed limits the total sample size to the "Pass" column (total passed = 80). The target event is being in Group A who passed (36).
Conditional Probability = \(\frac{36}{80} = \frac{9}{20}\).

Data Champions Answer Key Page 2 of 4

Data Lab: Independent Key Part I Page 3 of 4

Practice Sheet Q1 • Continuous Variables Correct Choice: B

Expanse of Core Logic: Continuous variables represent quantities obtained by measuring. CPU Temperature is measured dynamically and can take any decimal value (e.g., 142.56 F). Number of servers and IP addresses are counted in whole integers (discrete), and hard drive classification is categorical.

Practice Sheet Q2 • Range of Data Correct Choice: B

Expanse of Core Logic: Range is the difference between the absolute maximum and minimum values in a dataset.
Max value = 9. Min value = 4.
Range = \(9 - 4 = 5\).

Practice Sheet Q3 • Weighted/Mean Additions Correct Choice: D

Expanse of Core Logic:
Sum of 6 weights = \(6 \times 12 \text{ tons} = 72 \text{ tons}\).
Sum of 7 weights = \(7 \times 13 \text{ tons} = 91 \text{ tons}\).
Weight of the 7th container = \(91 - 72 = 19 \text{ tons}\).

Practice Sheet Q4 • Resistance to Outliers Correct Choice: B

Expanse of Core Logic: The median is highly resistant to extreme values (outliers). For {14, 15, 15, 17, 18, 19, 20, 45}, the median is 17.5. Without 45, the median is 17. The mean, range, and standard deviation are heavily influenced by the extreme outlier 45.

Practice Sheet Q5 • Interquartile Range (IQR) Correct Choice: B

Expanse of Core Logic: Dataset: {2, 4, 5, 8, 9, 12, 15}. Median is 8.
Lower half: {2, 4, 5} → Median (\(Q_1\)) = 4.
Upper half: {9, 12, 15} → Median (\(Q_3\)) = 12.
\(\text{IQR} = Q_3 - Q_1 = 12 - 4 = 8\).

Data Champions Answer Key Page 3 of 4

Data Lab: Independent Key Part II Page 4 of 4

Practice Sheet Q6 • Weighted Averages Correct Choice: B

Expanse of Core Logic: Weighted formula: \((75 \times 0.40) + (90 \times 0.40) + (85 \times 0.20)\).
\(30.0 + 36.0 + 17.0 = 83.0\).
Hence, the final weighted score of the subcontractor is exactly 83.

Practice Sheet Q7 • Primes and Multiples Correct Choice: C

Expanse of Core Logic: Outcomes in sample space S = {1, 2, 3, 4, 5, 6, 7, 8}.
Prime numbers are {2, 3, 5, 7}. Multiples of 4 are {4, 8}.
Union of both sets (Prime OR Multiple of 4) = {2, 3, 4, 5, 7, 8} (6 unique outcomes).
Probability = \(\frac{6}{8} = \frac{3}{4}\).

Practice Sheet Q8 • Table Probabilities Correct Choice: A

Expanse of Core Logic:
\(P(\text{Laptop}) = \frac{50}{100}\). \(P(\text{Defective}) = \frac{8}{100}\).
Overlapping event (Laptop AND Defective) = \(\frac{3}{100}\).
\(P(\text{Laptop } \cup \text{ Defective}) = \frac{50}{100} + \frac{8}{100} - \frac{3}{100} = \frac{55}{100} = \frac{11}{20}\).

Practice Sheet Q9 • Independent Replacement Correct Choice: A

Expanse of Core Logic: Draws are independent because the token is replaced.
1st draw: \(P(\text{Red}) = \frac{5}{10} = \frac{1}{2}\).
2nd draw: \(P(\text{Red}) = \frac{5}{10} = \frac{1}{2}\).
Compound probability = \(\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\).

Practice Sheet Q10 • Conditional Accounts Correct Choice: A

Expanse of Core Logic: "Given that... Active" limits the denominator to active accounts: \(25 \text{ (Premium)} + 35 \text{ (Basic)} = 60\). The numerator is Active Premium accounts (25).
Conditional Probability = \(\frac{25}{60} = \frac{5}{12}\).

Data Champions Answer Key Page 4 of 4