Probability from Two-Way Tables Worksheet | 7th Grade PDF Worksheets - Free Printable

Let’s solve each problem step by step.

---

Problem 1: Levi’s lunch survey

Table:
```
Boys Girls
Packed lunch 5 9
School dinners 8 6
```

a. How many people are there in Levi’s class?
Add all the numbers:
5 (boys packed) + 9 (girls packed) + 8 (boys school) + 6 (girls school) =
5 + 9 = 14; 8 + 6 = 14; 14 + 14 = 28

b. How many girls in Levi’s class have packed lunch?
Look at “Girls” column and “Packed lunch” row → 9

c. How many boys are there in Levi’s class?
Boys with packed lunch (5) + boys with school dinners (8) = 5 + 8 = 13

d. What fraction of the class are girls?
Total girls = 9 (packed) + 6 (school) = 15
Total class = 28
Fraction = 15/28

e. What percentage of the class have school dinners?
School dinners total = 8 (boys) + 6 (girls) = 14
Percentage = (14 ÷ 28) × 100 = 0.5 × 100 = 50%

---

Problem 2: Evelyn’s music survey

Table:
```
Jazz Hip Hop Girls
Adults 12 4 11
Children 2 14 15
```

Wait — this table is confusing. The columns are labeled “Jazz”, “Hip Hop”, and “Girls”. But “Girls” doesn’t fit as a music type. Also, rows are “Adults” and “Children”.

Looking again — it seems like the third column might be mislabeled. Probably, it should be “Rock” or another genre? But the questions mention “rock”, so likely the third column is meant to be “Rock”, not “Girls”. That must be a typo in the table.

Assuming the table is:

```
Jazz Hip Hop Rock
Adults 12 4 11
Children 2 14 15
```

That makes sense with the questions asking about rock.

So let’s proceed with that correction.

a. How many adults preferred jazz?
→ Look at Adults row, Jazz column → 12

b. How many children did Evelyn ask in total?
Children: Jazz (2) + Hip Hop (14) + Rock (15) = 2 + 14 = 16; 16 + 15 = 31

c. How many people preferred hip hop?
Hip Hop: Adults (4) + Children (14) = 4 + 14 = 18

d. What is the probability of selecting someone at random who prefers rock?
Total people = Adults (12+4+11=27) + Children (2+14+15=31) = 27 + 31 = 58
Rock lovers = 11 (adults) + 15 (children) = 26
Probability = 26 / 58 → simplify: divide numerator and denominator by 2 → 13/29

e. What is the probability of selecting an adult at random who prefers rock?
This means: given you pick an adult, what’s the chance they prefer rock?

Total adults = 12 + 4 + 11 = 27
Adults who prefer rock = 11
Probability = 11/27

*(Note: If the question meant “selecting someone at random who is an adult AND prefers rock”, then it would be 11/58. But the wording says “selecting an adult at random who prefers rock” — which implies conditional on being an adult. So 11/27 is correct.)*

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Problem 3: Teachers’ ages by subject

Table:
```
Subject 21-30 31-40 41-50 51+
Maths 12 9 14 6
English 15 10 7 11
Science 13 16 8 9
P.E. 7 3 1 0
History 4 8 9 8
```

a. How many science teachers are aged 41 - 50?
Look at Science row, 41-50 column → 8

b. How many teachers are aged 51 or over?
Add up the “51+” column:
Maths: 6
English: 11
Science: 9
P.E.: 0
History: 8
Total = 6 + 11 = 17; 17 + 9 = 26; 26 + 0 = 26; 26 + 8 = 34

c. Use the table to support the theory that P.E teachers are younger than other teachers. (hint: use percentages)

First, find total P.E. teachers:
7 (21-30) + 3 (31-40) + 1 (41-50) + 0 (51+) = 11

Now, how many are under 41? That’s 21-30 and 31-40: 7 + 3 = 10

Percentage of P.E. teachers under 41: (10 ÷ 11) × 100 ≈ 90.9%

Now compare to another subject, say Maths:

Total Maths teachers: 12 + 9 + 14 + 6 = 41

Under 41: 12 + 9 = 21

Percentage: (21 ÷ 41) × 100 ≈ 51.2%

Or English: total = 15+10+7+11 = 43; under 41 = 15+10=25; % = 25/43 ≈ 58.1%

Science: total = 13+16+8+9=46; under 41=13+16=29; % = 29/46 ≈ 63%

History: total=4+8+9+8=29; under 41=4+8=12; % = 12/29 ≈ 41.4%

So P.E. has 90.9% under 41, while others range from 41% to 63%. This supports the idea that P.E. teachers are younger.

We can also note: no P.E. teacher is 51+, while other subjects have several.

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Final Answer:

1)
a. 28
b. 9
c. 13
d. 15/28
e. 50%

2)
a. 12
b. 31
c. 18
d. 13/29
e. 11/27

3)
a. 8
b. 34
c. About 90.9% of P.E. teachers are under 41, compared to less than 65% for other subjects, supporting that P.E. teachers are younger.