Probability: Sample Spaces, Independence and Conditional Probability: Algebra 2 Math Test – PDF Download

Question 1: Sample space of coin flips (2 points)

A fair coin is flipped three times .

1. List all outcomes in the sample space. (1 point)
2. Let \(A\) be “exactly two heads”. List the outcomes in \(A\) and find \(P(A)\). (1 point)

Question 2: Events from a set of numbers (2 points)

A number is chosen at random from \(1,2,3,…,12\) written on slips. Let \(A\) be “even number” and \(B\) be “multiple of \(3\)”.

1. List the outcomes in “\(A\) and \(B\)” and in “\(A\) or \(B\)”. (1 point)
2. Find \(P(A\text{ or }B)\) and \(P(\text{not }A)\). (1 point)

Question 3: Addition rule with a Venn diagram (2 points)

The Venn diagram shows \(40\) students in choir and drama. One student is chosen at random.

1. Find \(P(\text{choir})\), \(P(\text{drama})\) and \(P(\text{choir and drama})\). (1 point)
2. Use the addition rule to find \(P(\text{choir or drama})\), then find \(P(\text{neither})\). (1 point)

Question 4: Independent or not (2 points)

Events \(A\) and \(B\) have \(P(A)=0.3\) and \(P(B)=0.6\).

1. If \(P(A\text{ and }B)=0.18\), are \(A\) and \(B\) independent? Justify your answer. (1 point)
2. If instead \(P(A\text{ and }B)=0.2\), find \(P(A|B)\). (1 point)

Question 5: Two-way table of lunches (3 points)

The table shows \(120\) students by grade and lunch type. One student is chosen at random.

1. Find \(P(\text{school lunch})\). (1 point)
2. Find \(P(\text{10th}\,|\,\text{packed lunch})\). (1 point)
3. Are “9th grade” and “school lunch” independent? Justify your answer. (1 point)

Question 6: Pens without replacement (3 points)

A box holds \(4\) black pens and \(2\) white pens. Two pens are drawn without replacement. The tree shows the probabilities.

1. Find the probability that both pens are black. (1 point)
2. Find the probability that the pens have different colors. (1 point)
3. Find the probability that the first pen is black, given that the second pen is white. (1 point)

Question 7: Free throws in a row (3 points)

Jamal makes \(80\%\) of his free throws, and his shots are independent. He takes two shots.

1. Find the probability that he makes both. (1 point)
2. Find the probability that he misses both. (1 point)
3. Find the probability that he makes at least one. (1 point)

Question 8: Conditional probability formula (2 points)

In a town, \(60\%\) of households have a dog (\(D\)), \(40\%\) have a cat (\(C\)), and \(25\%\) have both.

1. Find \(P(C|D)\). (1 point)
2. Find \(P(D|C)\). (1 point)

Question 9: At least one six (1 point)

A fair die is rolled twice. Find the probability of getting at least one \(6\).

⬇ Download the Algebra 2 Probability: Sample Spaces, Independence and Conditional Probability test (PDF, 97 KB)

See every chapter on the Algebra 2 math page.