Answer:
The probability is 28 out of 37: [tex]\frac{28}{37}[/tex]
Step-by-step 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: [tex]\frac{28}{37}[/tex]
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