A survey was conducted on the types of shoes worn by teachers at South Kitsap high school. The Venn diagram below summarizes the findings.A= represents all brown shoesB= represents all tennis shoes/sneakersC= represents all shoes over three years old What is the probability that a randomly selected teacher is wearing shoes over 3 years old Answer Choices:0.230.50.620.85

Question

26-10-2022
Mathematics

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A survey was conducted on the types of shoes worn by teachers at South Kitsap high school. The Venn diagram below summarizes the findings.A= represents all brown shoesB= represents all tennis shoes/sneakersC= represents all shoes over three years old What is the probability that a randomly selected teacher is wearing shoes over 3 years old Answer Choices:0.230.50.620.85

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SafwanS654672 SafwanS654672 · Answer 1 · 2022-10-26T14:39:23+02:00

Answer:

0.48

Explanation:

We were given the following details:

A= represents all brown shoes

B= represents all tennis shoes/sneakers

C= represents all shoes over three years old

Number of teachers wearing all brown shoes = 15 + (5 - 3) + (7 - 3) + 3 = 15 + 2 + 4 + 3 = 24

Number of teachers wearing shoes over 3 years old = 20 + (20 - 3) + (7 - 3) + 3 = 20 + 17 + 4 + 3 = 44

Total number of teachers = 15 + 30 + 20 + (5 - 3) + (20 - 3) + (7 - 3) + 3 = 65 + 2 + 17 + 4 + 3 = 91

The probability that a randomly selected teacher is wearing shoes over 3 years old is given by:

[tex]\begin{gathered} P=\frac{Number\text{ of teachers wearing shoes over 3 years old}}{Total\text{ Number of teachers}} \\ P=\frac{44}{91} \\ P=0.48 \\ \\ \therefore P=0.48 \end{gathered}[/tex]

Therefore, the probability that a randomly selected teacher is wearing shoes over 3 years old is 0.48