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The mathematics department of a college has 15 male professors, 9 female professors, 6 male teaching assistants, and 12 female teaching assistants. if a person is selected of random from the group, find the probability that the selected person is a professor or a male. The probability is?

Answer :

Given:

The number of male professors = 15.

The number of female professors = 9.

The number of male teaching assistants = 6.

The number of female teaching assistants = 12.

A person is selected randomly from the group.

Required:

We need to find the probability that the selected person is a professor or a male.

Explanation:

The total number of people in the group = 15+9+6+12 = 42

n(S) =The total number of people in the group

[tex]n(S)=42[/tex]

Let A be the event that the selected person is a professor or a male.

The number of people who are professors or male = 15+9+6 = 30

n(A)= The number of people who are professors or male.

[tex]n(A)=30[/tex]

Let P(A) be the probability that the selected person is a professor or a male.

[tex]P(A)=\frac{n(A)}{n(S)}[/tex][tex]P(A)=\frac{30}{42}[/tex][tex]P(A)=\frac{15}{21}=\frac{5}{7}[/tex]

Final answer:

The probability that the selected person is a professor or a male is 5/7.

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