Question

Of 50 people, 38 have brown hair, 29 have brown eyes, and 23 have both brown hair and brown eyes. how many have neither brown hair nor brown eyes?
A) 6 C) 10
B) 8 D) 12

Answer 1

Answer:

The correct option is A.

Step-by-step explanation:

Let A and B represents the following events.

A = Person have brown hair

B = Person have brown eyes

Given information:

Total people, S = 50

Person have brown hair, n(A)=38

Person have brown eyes, n(B)=29

Person have both brown hair and brown eyes, n(A∩B)=23.

The total number of persons have either brown hair or brown eyes is

$n(A\cup B)=n(A)+n(B)+n(A\cap B)$

$n(A\cup B)=38+29-23$

$n(A\cup B)=44$

The number of persons have neither brown hair nor brown eyes is

$S-n(A\cup B)=50-44=6$

Total 6 persons have neither brown hair nor brown eyes.

Therefore the correct option is A.

Answer 2

The number of people with neither brown hair nor brown eyes is equal to: A. 6 people.

How to calculate the number of people with neither brown hair nor brown eyes?

• Let A represent people with brown hair.

• Let B represent people with brown eyes.

Given the following data:

Total population, T = 50 people.

People with brown hair, n(A) = 38 people.

People with brown eyes, n(B) = 29 people.

People with both brown hair and eyes, n(A∩B) = 23 people.

Mathematically, the total number of people with either brown hair or eyes is given by:

n(A ∪ B) = n(A) + n(B) - n(A∩B)

n(A ∪ B) = [38 + 29] - 23

n(A ∪ B) = 67 - 23

n(A ∪ B) = 44 people.

Now, we can determine the number of people with neither brown hair nor brown eyes:

B' = T - n(A ∪ B)

B' = 50 - 44

B' = 6 people.

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