Practice reading two-way tables, finding conditional probabilities, and deciding whether two events are independent.
Read each problem carefully. Show your work in the space provided. Write probabilities as fractions, decimals, or percents when appropriate.
Using counts to find conditional probabilities
Statistics - Grade 9-12
- 1
A class survey of 60 students is shown. Juniors: 18 play sports, 12 do not play sports, 30 total. Seniors: 15 play sports, 15 do not play sports, 30 total. Totals: 33 play sports, 27 do not play sports, 60 total. Find P(plays sports | junior).
- 2
Use the same class survey. Find P(senior | does not play sports).
- 3
A reading survey of 120 students is shown. Reads daily: 28 like mystery books, 12 do not like mystery books, 40 total. Does not read daily: 32 like mystery books, 48 do not like mystery books, 80 total. Totals: 60 like mystery books, 60 do not like mystery books, 120 total. Find P(reads daily and likes mystery books) and P(likes mystery books | reads daily).
- 4
Use the reading survey from Problem 3. Decide whether liking mystery books and reading daily appear to be independent events.
- 5
A transportation table for 200 students is partly missing. 9th grade: 54 use the bus, 46 do not use the bus, 100 total. 10th grade: 36 use the bus, missing number do not use the bus, 100 total. Totals: 90 use the bus, 110 do not use the bus, 200 total. Find the missing number and find P(uses the bus | 10th grade).
- 6
A club survey of 75 members is shown. Owns a tablet: 20 have a phone case, 10 do not have a phone case, 30 total. Does not own a tablet: 15 have a phone case, 30 do not have a phone case, 45 total. Totals: 35 have a phone case, 40 do not have a phone case, 75 total. If a member has a phone case, find the probability that the member owns a tablet.
- 7
Use the club survey from Problem 6. Decide whether owning a tablet and having a phone case appear to be independent events.
- 8
An after-school survey is shown. Has a quiet study space: 64 completed homework, 16 did not complete homework, 80 total. No quiet study space: 36 completed homework, 24 did not complete homework, 60 total. Totals: 100 completed homework, 40 did not complete homework, 140 total. Compare P(completed homework | has a quiet study space) and P(completed homework | no quiet study space).
- 9
Use the after-school survey from Problem 8. If a student completed homework, find the probability that the student had a quiet study space.
- 10
In a sample of 500 drivers, 300 wear seat belts and 200 do not wear seat belts. Of the drivers who wear seat belts, 270 stop completely at a stop sign. Of the drivers who do not wear seat belts, 150 stop completely. Find P(stops completely | does not wear a seat belt) and P(does not wear a seat belt | stops completely).
- 11
A group has 160 students. There are 70 students in band and 90 students not in band. Of the band students, 80% own an instrument. Of the non-band students, 30% own an instrument. Complete the counts and find P(in band | owns an instrument).
- 12
A medical screening table for 1,000 people is shown. Has the condition: 45 positive test results, 5 negative test results, 50 total. Does not have the condition: 90 positive test results, 860 negative test results, 950 total. Totals: 135 positive test results, 865 negative test results, 1,000 total. Find P(has the condition | positive test result). Then explain why this is different from P(positive test result | has the condition).