Algebra 2 Conditional Probability and Independence Test with Point Values (PDF)

Algebra 2 math test: Conditional Probability and Independence – Maths PDF

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This probability test for Algebra 2 covers conditional probability and independence (Common Core S-CP.A.1, S-CP.A.2, S-CP.A.3, S-CP.A.4, S-CP.A.5, S-CP.B.6, S-CP.B.7, S-CP.B.8, S-CP.B.9), with a free PDF to print.

This 45-minute test on conditional probability and independence has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: Conditional Probability and Independence
Standards: S-CP.A.1, S-CP.A.2, S-CP.A.3, S-CP.A.4, S-CP.A.5, S-CP.B.6, S-CP.B.7, S-CP.B.8, S-CP.B.9
Time: 45 minutes
Total: 20 points

Probability test: questions

Question 1 – Sample space [2 pts]

Two fair dice are rolled. Find the probability that the sum is at least 10.

Question 2 – Union [2 pts]

30 students in two sports.

The Venn diagram shows 30 students. Find the probability that a random student plays soccer or track.

Question 3 – Two-way table [3 pts]

Bike ownership.

The table shows 100 students. Find P(owns a bike), P(owns a bike | girl), and decide whether owning a bike is independent of gender.

Question 4 – Independence check [2 pts]

For two events, \(P(A) = 0.6\), \(P(B) = 0.5\), and \(P(A \text{ and } B) = 0.35\). Are \(A\) and \(B\) independent?

Question 5 – Tree diagram [3 pts]

Two draws from a bag of 5 red (R) and 3 blue (B) marbles, without replacement.

A bag has 5 red and 3 blue marbles. Two are drawn without replacement. Find the probability that the marbles are different colors.

Question 6 – Counting [2 pts]

(a) In how many ways can a president, vice president, and treasurer be chosen from 7 students? (b) In how many ways can a team of 3 be chosen from 7 students?

Question 7 – At least one [2 pts]

A fair coin is flipped 4 times. Find the probability of at least one head.

Question 8 – Conditional probability [2 pts]

Of 200 customers, 80 buy coffee, 50 buy a muffin, and 30 buy both. Find P(buys a muffin | buys coffee).

Question 9 – Find the error [2 pts]

Jamal says that drawing two cards without replacement makes the events independent. Explain his error using the cards.

Key facts behind this probability test

Key facts

P(not A) = 1 – P(A); P(A or B) = P(A) + P(B) – P(A and B).
P(A given B) = P(A and B) / P(B).
Independent: P(A and B) = P(A)·P(B).
Multiplication rule: P(A and B) = P(A)·P(B given A).
Permutations P(n, r) = n!/(n – r)!; combinations C(n, r) = n!/(r!(n – r)!).

How to use this probability test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 2 chapters: Algebra 2 math.

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