In a survey of 500 scholars, 200 took tea and 300 took coffee. If 10 scholars took neither, how many took both?

Here are the solutions to the questions: Question 29: Step 1: Determine the number of scholars who took at least one of tea or coffee. Total scholars N(U) = 500. Scholars who did not take either N((T ∪ C)') = 10. The number of scholars who took at least one is N(T ∪ C) = N(U) − N((T ∪ C)'). N(T ∪ C) = 500 − 10 = 490 Step 2: Use the Principle of Inclusion-Exclusion to find the number of scholars who took both. Given N(T) = 200 (tea) and $N(

In a survey of 500 scholars, 200 took tea and 300 took coffee. If 10 scholars took neither, how many took both?

Here are the solutions to the questions: Question 29: Step 1: Determine the number of scholars who took at least one of tea or coffee. Total scholars N(U) = 500. Scholars who did not take either N((T ∪ C)') = 10. The number of scholars who took at least one is N(T ∪ C) = N(U) − N((T ∪ C)'). N(T ∪ C) = 500 − 10 = 490 Step 2: Use the Principle of Inclusion-Exclusion to find the number of scholars who took both. Given N(T) = 200 (tea) and $N(

Solved: In a survey of 500 scholars, 200 took tea and 300…

Here are the solutions to the questions:

Question 29:

Determine the number of scholars who took at least one of tea or coffee.
Total scholars $N(U) = 500$ .
Scholars who did not take either $N((T \cup C)') = 10$ .
The number of scholars who took at least one is $N(T \cup C) = N(U) - N((T \cup C)')$ .
$N(T \cup C) = 500 - 10 = 490$
Use the Principle of Inclusion-Exclusion to find the number of scholars who took both.
Given $N(T) = 200$ (tea) and $N(

In a survey of 500 scholars, 200 took tea and 300 took coffee. If 10 scholars took neither, how many took both?

Step-by-step solution

Determine the number of scholars who took at least one of tea or coffee.

Use the Principle of Inclusion-Exclusion to find the number of scholars who took both.

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