Question

The mathematics department of a college has 7 male​ professors, 6 female​ professors, 12 male teaching​ assistants, and 7 female teaching assistants. If a person is selected at random from the​ group, find the probability that the selected person is a professor or a male

Answer 1

Answer:

0.78125 or 78.125%

Step-by-step explanation:

Male professors = 7

Female professors = 6

Male T.A. = 12

Female T.A. = 7

Number of people in the department = 32

The probability that the selected person is a professor or a male is given by the probability that the person is a professor added to the probability that the person is a male, minus the probability that the person is a male professor:

$P( P\ or\ M) = P(P) +P(M) - P(P\ and\ M)\\P( P\ or\ M) =\frac{7+6}{32}+ \frac{7+12}{32}- \frac{7}{32} \\P( P\ or\ M) = 0.78125 = 78.125\%$

The probability is 0.78125 or 78.125%