he physics department of a college has 9 male professors, 8 female professors, 10 male teaching assistants, and 13 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a teaching assistant or a female
9+8+10+13 = total people =40 people
TEACHING ASSISTANT: 10+ 13 = 23 --> 23/40
FEMALE: 8+13 = 21 --> 21/40
11/10
To find the probability that the selected person is a teaching assistant or a female, we need to determine the total number of teaching assistants and the total number of females, and then find the probability by dividing the sum of these two numbers by the total number of people.
Total number of teaching assistants = 10 (male teaching assistants) + 13 (female teaching assistants) = 23
Total number of females = 8 (female professors) + 13 (female teaching assistants) = 21
Total number of people = 9 (male professors) + 8 (female professors) + 10 (male teaching assistants) + 13 (female teaching assistants)
= 40
Hence, the probability that the selected person is a teaching assistant or a female is given by:
Probability = (Total number of teaching assistants + Total number of females) / Total number of people
= (23 + 21) / 40
= 44 / 40
= 11 / 10
Therefore, the probability that the selected person is a teaching assistant or a female is 11/10 or 1.1 (in decimal form)
To find the probability that a selected person is a teaching assistant or a female, we need to calculate the probability of two mutually exclusive events: being a teaching assistant and being a female.
Event A: Being a teaching assistant = 10 male teaching assistants + 13 female teaching assistants = 23 teaching assistants.
Event B: Being a female = 8 female professors + 13 female teaching assistants = 21 females.
We can add these two probabilities together, but we need to subtract the probability of the intersection of these two events (i.e., the probability of being a female teaching assistant) to avoid double counting.
Event C: Being a female teaching assistant = 13 female teaching assistants.
To calculate the probability, we divide the total number of outcomes (people) in our sample space by the total number of possible outcomes. The total number of people is the sum of the professors and teaching assistants: 9 male professors + 8 female professors + 10 male teaching assistants + 13 female teaching assistants = 40 people.
Therefore, the probability of selecting a person who is a teaching assistant or a female is:
P(A or B) = (A + B) - C / Total number of people
= (23 + 21) - 13 / 40
= 31 / 40
So, the probability that the selected person is a teaching assistant or a female is 31/40 or 0.775.