Two events are independent when knowing one tells you nothing about the other, and that has a test you can run: the share who are BOTH should be the share who are A times the share who are B. These free printable worksheets give the table and ask for the verdict.
Every survey on these sheets is of exactly 100 people, and that is deliberate rather than lazy: at a total of a hundred the counts in the table already ARE percents, so the comparison is between two numbers a student can read and multiply without a division in the way. The arithmetic is not what this standard is about — noticing that the overlap can be PREDICTED from the two margins is.
Why this sheet works
Half of every page is independent and half is not. A sheet where the answer is the same every time is one a student can pass without looking, so both verdicts are always dealt.
How this one works
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Multiply the two percents. Does the table agree? Circle your answer.
1
Won
Lost
Total
Team A
28
12
40
Team B
42
18
60
Total
70
30
100
Are Team A and Won independent?
IndependentNot independent
2
Pet
No pet
Total
Grade 7
20
20
40
Grade 8
30
30
60
Total
50
50
100
Are Grade 7 and Pet independent?
IndependentNot independent
3
Swim
Hike
Total
Morning
56
14
70
Afternoon
24
6
30
Total
80
20
100
Are Morning and Swim independent?
IndependentNot independent
4
Cash
Card
Total
Weekday
49
21
70
Weekend
21
9
30
Total
70
30
100
Are Weekday and Cash independent?
IndependentNot independent
5
Cash
Card
Total
Weekday
15
35
50
Weekend
45
5
50
Total
60
40
100
Are Weekday and Cash independent?
IndependentNot independent
6
Chess
Cards
Total
Juniors
3
57
60
Seniors
27
13
40
Total
30
70
100
Are Juniors and Chess independent?
IndependentNot independent
Independent events · Clear casesAnswer key
1. Are Team A and Won independent? → Independent — 40% × 70% = 28%, and the table shows 28%2. Are Grade 7 and Pet independent? → Independent — 40% × 50% = 20%, and the table shows 20%3. Are Morning and Swim independent? → Independent — 70% × 80% = 56%, and the table shows 56%4. Are Weekday and Cash independent? → Independent — 70% × 70% = 49%, and the table shows 49%5. Are Weekday and Cash independent? → Not independent — 50% × 60% = 30%, and the table shows 15%6. Are Juniors and Chess independent? → Not independent — 60% × 30% = 18%, and the table shows 3%
