P9a - Conditional probabilities - BossMaths.com - Free Printable

Let’s solve each part step by step.

We are told that 100 people were surveyed. The Venn diagram shows how many like Chocolate, Vanilla, and Strawberry — including overlaps.

The numbers in the diagram:

- Only Chocolate: 30
- Only Vanilla: 16
- Only Strawberry: 8
- Chocolate & Vanilla only (not Strawberry): 21
- Chocolate & Strawberry only (not Vanilla): 2
- Vanilla & Strawberry only (not Chocolate): 5
- All three flavors: 14
- Outside all circles (like none): 4

Let’s verify total adds to 100:

30 + 16 + 8 + 21 + 2 + 5 + 14 + 4 =
30+16=46; 46+8=54; 54+21=75; 75+2=77; 77+5=82; 82+14=96; 96+4=100 → ✔ Correct.

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a) How many people like vanilla?

Vanilla includes:
- Only Vanilla: 16
- Vanilla & Chocolate only: 21
- Vanilla & Strawberry only: 5
- All three: 14

Add them: 16 + 21 + 5 + 14 =
16+21=37; 37+5=42; 42+14=56

→ 56 people like vanilla

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b) How many people don’t like any of the flavours?

This is the number outside all circles → given as 4

→ 4 people

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c) Find the probability that a random respondent likes chocolate ice cream.

First, find how many like chocolate:

Chocolate includes:
- Only Chocolate: 30
- Chocolate & Vanilla only: 21
- Chocolate & Strawberry only: 2
- All three: 14

Add: 30 + 21 + 2 + 14 =
30+21=51; 51+2=53; 53+14=67

So, 67 out of 100 like chocolate.

Probability = 67/100 = 0.67 or 67%

But since it says “find the probability”, we can leave it as a fraction: 67/100

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d) Find the probability that a random respondent likes strawberry but not vanilla ice cream.

“Strawberry but not vanilla” means:

- Only Strawberry: 8
- Strawberry & Chocolate only (not Vanilla): 2

Do NOT include those who also like vanilla (so exclude the 5 and 14).

So: 8 + 2 = 10

Total respondents: 100

Probability = 10/100 = 1/10 or 0.1

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Final Answer:

a) 56
b) 4
c) 67/100
d) 1/10