This 45-minute test covers probability for Geometry: events and Venn diagrams, independence, two-way tables, conditional probability, counting, fair decisions and the analysis of a medical test. It has 9 questions worth 20 points. Calculators are allowed; show your work.
- Grade: Geometry
- Chapter: Probability: Independence, Conditional Probability and Fair Decisions
- 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, S-MD.B.6, S-MD.B.7
- Time: 45 minutes
- Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 3 pts; Question 4: 2 pts; Question 5: 2 pts; Question 6: 3 pts; Question 7: 2 pts; Question 8: 3 pts; Question 9: 1 pt)
Question 1: Two clubs on a Venn diagram (2 points)
In a class of 30 students, 14 are in band, 11 are in orchestra and 4 are in both.
- How many students are in neither group? (1 point)
- Find the probability that a randomly chosen student is in band or orchestra. (1 point)
Question 2: Independence and the addition rule (2 points)
For events A and B, \(P(A)=0.35,\ P(B)=0.6\) and \(P(A\text{ and }B)=0.21\).
- Are A and B independent? Justify. (1 point)
- Find P(A or B). (1 point)
Question 3: Honey sales and age (3 points)
At a farmers market, 200 shoppers were asked whether they bought honey.
- Find P(bought honey given under 30). (1 point)
- Find P(30 and over given bought honey). (1 point)
- Is buying honey independent of age group? Justify. (1 point)
Question 4: Two jellybeans (2 points)
A jar holds 6 red and 4 yellow jellybeans. Two are drawn at random without replacement.
- Find the probability that both are red. (1 point)
- Find the probability that they are different colors. (1 point)
Question 5: Swim meet counting (2 points)
Nine swimmers enter a race.
- In how many ways can first, second and third place be awarded? (1 point)
- In how many ways can 3 of the 9 swimmers be chosen for a relay team? (1 point)
Question 6: Choosing three students (3 points)
A teacher chooses 3 students at random from a group of 8 girls and 6 boys.
- Find the probability that all three are girls. (2 points)
- Find the probability that at least one is a boy. (1 point)
Question 7: Choosing with a spinner (2 points)
Mei and Noah decide who washes the dishes by spinning the fair spinner with 8 equal sectors. Rule 1: Mei washes if the result is prime; otherwise Noah washes. Rule 2: Mei washes if the result is greater than 5; otherwise Noah washes.
- Is Rule 1 fair? Justify. (1 point)
- Is Rule 2 fair? Justify. (1 point)
Question 8: Screening test (3 points)
A condition affects 4% of 5,000 people. The test is positive for 90% of people who have it and for 6% of people who do not.
- Find the two numbers of positive tests. (1 point)
- Find P(positive test). (1 point)
- Find P(condition given positive test). (1 point)
Question 9: Switching doors (1 point)
A car is hidden behind one of three doors and goats behind the other two. A contestant picks a door. The host, who knows where the car is, opens a different door with a goat and offers a chance to switch. Find the probability of winning the car by switching.
See every chapter on the Geometry math page.