Question

The math department of a college has 5 male professors, 14 female professors, 5 males 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.

What is the probability?

Answer 1

If their math department is asking you to work that out then it's a pretty bad math department... But
Work out the total number of people: 5 + 14 + 5 + 13 = 37
Chance of a female teacher: 14/37
Chance of a male teaching assistant: 5/37
Chance of a female teaching assistant: 13/37
14/37 + 5/37 + 13/37 = 32/37 chance

Answer 2

The probability is 28 out of 37:
`(28)/(37)`

Explanation:

Compatible events are those that can happen at the same time, since they have, at least, a common element, as in this case, which can occur, for example, that the chosen person is an auxiliary teacher or a woman.

In these cases the probability is calculated with the law of addition, which says:

P(A or B) = P(A) + P(B) - P(A and B)

You know that there are 5 male professors, 14 female professors, 5 male teaching assistants and 12 female teaching assistants

So, with this data you can calculate:

The probability of being a teaching assistant (regardless of being male or female) such as:

P(teaching assistant) = 5+13 = 18

The probability of being a female (regardless of being professors or teaching assistants) such as:

P(males) = 14+13 = 23

The probability of being teaching assistant and a female such as:

P(teaching assistant AND a female)=13

So, finally you can get:

P(teaching assistant OR female)=P(teaching assistant)+P(female)-P(teaching assistant AND a female)

P(teaching assistant OR female)=18+23-13

P(teaching assistant OR female)=28

Knowing that:

P(people to choose from) = 5+14+5+13 = 37

The probability is 28 out of 37:
`(28)/(37)`

N(people to choose from) = 6+11+10+12 = 39

The probability is 27 out of 39 = 27/39 which reduces to 9/13

Edwin