In a survey of 150 people, 80 people like tea, 60 like coffee, and 30 like both tea and coffee. How many people like only coffee? Options 10 30 20 40

1. Break Down the Problem

To find the number of people who like only coffee, we can use the principle of inclusion-exclusion. We know:

• Total people surveyed: $n = 150$
• People who like tea: $T = 80$
• People who like coffee: $C = 60$
• People who like both tea and coffee: $B = 30$

We need to find the number of people who like only coffee, denoted as $C_{only}$.

2. Relevant Concepts

Using the formula for people who like only one of the options: $C_{only} = C - B$ where $C$ is the total people who like coffee, and $B$ is the number of people who like both.

3. Analysis and Detail

Now we can apply the numbers from our problem: $C_{only} = 60 - 30 = 30$

4. Verify and Summarize

We found that $C_{only} = 30$. This means 30 people exclusively like coffee.

Final Answer

The number of people who like only coffee is $30$.