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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

Respuesta :

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

[tex]n(A\cup B)=n(A)+n(B)+n(A\cap B)[/tex]

[tex]n(A\cup B)=38+29-23[/tex]

[tex]n(A\cup B)=44[/tex]

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

[tex]S-n(A\cup B)=50-44=6[/tex]

Total 6 persons have neither brown hair nor brown eyes.

Therefore the correct option is A.

Lanuel

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.

Read more on Venn diagram here: https://brainly.com/question/24581814

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