AP Statistics Conditional Probability and Independence Test Solutions and Scoring (PDF)

AP Statistics math test solutions: Conditional Probability and Independence – Maths PDF

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This conditional probability test answers for AP Statistics covers conditional probability and independence (Common Core AP STAT 4.5, AP STAT 4.6, HSS-CP.A.2, HSS-CP.A.3, HSS-CP.A.4, HSS-CP.B.6, HSS-CP.B.8), with a free PDF to print.

Each solution includes a scoring guide. Award points for the correct denominator, the correct multiplication along branches, and a clear conclusion about independence in context.

AP Statistics · Common Core State Standards: AP STAT 4.5, AP STAT 4.6, HSS-CP.A.2, HSS-CP.A.3, HSS-CP.A.4, HSS-CP.B.6, HSS-CP.B.8

Conditional probability test answers: worked solutions

Question 1 – Conditional from a table [3 pts]

Opinion by sex.

(a) \(\frac{36}{60}=0.6\). (b) \(\frac{36}{60}=0.6\). (c) P(likes) = 60/100 = 0.6 = P(likes | girl) = P(likes | boy) = 24/40 = 0.6.

0.6; 0.6; yes, independent.

Scoring: 1 point per part.

Question 2 – Tree diagram [4 pts]

A tree for bus arrival.

(a) \(0.3\times 0.4=0.12\). (b) \(0.12+0.07=0.19\). (c) \(\frac{0.12}{0.19}\approx 0.632\).

0.12; 0.19; 0.632.

Scoring: 1 point each for (a) and (b); 1 point for the setup and 1 point for 0.632 in (c).

Question 3 – Independence [3 pts]

(a) \(0.5+0.2-0.6=0.1\). (b) \(0.5\times 0.2=0.1\), so yes. (c) No, since P(A and B) = 0.1 is not 0.

0.1; independent; not mutually exclusive.

Scoring: 1 point per part.

Question 4 – Without replacement [2 pts]

\(\frac{5}{8}\times\frac{4}{7}=\frac{20}{56}=\frac{5}{14}\).

5/14, about 0.357.

Scoring: 1 point for the two fractions, 1 point for the product.

Question 5 – At least one [2 pts]

Miss both: \(0.25^{2}=0.0625\). At least one: \(1-0.0625=0.9375\).

0.9375.

Scoring: 1 point for the complement, 1 point for 0.9375.

Question 6 – Explain the difference [2 pts]

A and B can occur together (rolling a 6 is even), so they are not mutually exclusive. P(B | A) = 1/3 but P(B) = 1/6, so they are not independent either.

Independent: P(B | A) = P(B). Mutually exclusive: they cannot both happen.

Scoring: 1 point for each correct explanation.

Question 7 – Medical test [3 pts]

\(P(+)=0.05(0.90)+0.95(0.08)=0.045+0.076=0.121\). \(P(C\mid +)=\frac{0.045}{0.121}\approx 0.372\).

0.121 and about 0.372.

Scoring: 1 point for the two products, 1 point for P(positive), 1 point for the conditional.

Question 8 – Read the notation [1 pt]

Independence check.

It is the probability that it rained, given that the bus was late.

The probability of rain given a late bus.

Scoring: 1 point for a correct reading that conditions on ‘late’.

Total score

Total

20 points

Key facts behind this conditional probability test answers

Key facts

P(A | B) = P(A and B) / P(B): restrict to the outcomes where B occurred.
General multiplication rule: P(A and B) = P(B) P(A | B).
Independent: P(A | B) = P(A), so P(A and B) = P(A) P(B).
Mutually exclusive events with positive probabilities are never independent.
Tree diagrams multiply along branches and add the paths that fit the event.

How to use this conditional probability test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All AP Statistics chapters: AP Statistics math.

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