This geometry probability test answer key gives the full solution and the scoring guide for each of the 9 test questions on probability: independence, conditional probability and fair decisions.
This answer key shows the worked solution and the scoring guide for every question of the probability test. Award the points as described, give partial credit for correct setups, and total the score out of 20.
Geometry Probability Test Answer Key: questions 1–5
Question 1: Two clubs on a Venn diagram (2 points)
(a) Band or orchestra: \(14+11-4=21\). Neither: \(30-21=9\).
(b) \(\frac{21}{30}=\frac{7}{10}\).
Scoring: 1 point for 9 (accept 9 from a correct diagram); 1 point for \(\frac{7}{10}\) or 0.7.
Question 2: Independence and the addition rule (2 points)
(a) \(0.35\times 0.6=0.21=P(A\text{ and }B)\), so A and B are independent.
(b) \(0.35+0.6-0.21=0.74\).
Scoring: 1 point for comparing the product with P(A and B) and concluding independent; 1 point for 0.74.
Question 3: Honey sales and age (3 points)
(a) \(\frac{36}{100}=\frac{9}{25}\).
(b) \(\frac{54}{90}=\frac{3}{5}\).
(c) \(P(\text{honey})=\frac{90}{200}=0.45\neq 0.36=P(\text{honey}\mid\text{under }30)\), so not independent.
Scoring: 1 point per part; in (a) and (b) the correct denominator (100, then 90) earns the point, and (c) needs a numerical comparison.
Question 4: Two jellybeans (2 points)
(a) \(\frac{6}{10}\cdot\frac{5}{9}=\frac{30}{90}=\frac{1}{3}\).
(b) Red then yellow: \(\frac{6}{10}\cdot\frac{4}{9}=\frac{24}{90}\); yellow then red is equal. Total \(\frac{48}{90}=\frac{8}{15}\).
Scoring: 1 point for each part; in (b) the point requires both orders.
Question 5: Swim meet counting (2 points)
(a) \(_{9}P_{3}=9\cdot 8\cdot 7=504\).
(b) \(_{9}C_{3}=\frac{504}{6}=84\).
Scoring: 1 point per part.
Geometry Probability Test Answer Key: questions 6–9
Question 6: Choosing three students (3 points)
(a) \(\frac{_{8}C_{3}}{_{14}C_{3}}=\frac{56}{364}=\frac{2}{13}\).
(b) Complement: \(1-\frac{2}{13}=\frac{11}{13}\).
Scoring: (a) 1 point for 56 and 364, 1 point for \(\frac{2}{13}\); (b) 1 point for using the complement.
Question 7: Choosing with a spinner (2 points)
(a) Primes: 2, 3, 5, 7, so \(P(\text{Mei})=\frac{4}{8}=\frac{1}{2}\). Fair.
(b) Results 6, 7, 8: \(P(\text{Mei})=\frac{3}{8}\) and \(P(\text{Noah})=\frac{5}{8}\). Not fair.
Scoring: 1 point per part, with the probabilities shown.
Question 8: Screening test (3 points)
(a) Condition: \(5000\times 0.04=200\) people, \(0.9\times 200=180\) positive. No condition: \(4800\) people, \(0.06\times 4800=288\) positive.
(b) \(\frac{180+288}{5000}=\frac{468}{5000}=0.0936\).
(c) \(\frac{180}{468}=\frac{5}{13}\approx 0.385\).
Scoring: 1 point per part.
Question 9: Switching doors (1 point)
The first pick is correct with probability \(\frac{1}{3}\). Switching wins exactly when the first pick was wrong, so \(\frac{2}{3}\).
Scoring: 1 point for \(\frac{2}{3}\) with a reason; 0 points for an answer with no reason.
Scoring summary
20 points: add the points of every question of this geometry probability test answer key.
How to use this geometry probability test answer key
Use this geometry probability test answer key to score the test fairly and to see which skills need more practice.
Printable PDF · Test Answer Key
Geometry Probability: Independence, Conditional Probability and Fair Decisions test answer key
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