# Probability Problem

#### moniker

##### New member
Hello, Im new here and Im stuck doing this problem since the probability module only mentioned:
- Union Events
- Intersection Events
- Mutually exclusive Events

Im not sure how to use them on this problem

10 radiologists and 15 nurses apply for positions in a hospital.
If 5 applicants are hired at random, what is the probability that:

a) all applicants are nurses?
b) two are radiologists and three are nurses?
c) four are nurses and one is a radiologist?
d) at least three are nurses?
e) at most two are radiologists?

Searching them on google/youtube just made me more confused mentioning alot of Events that arent mentioned in the module, making it more complicated for me to understand

All I wanna know is how do I solve this problem if I will follow only the contents of the module I have?
When I asked around, they give me different solutions outside of the module so I don't know...

Thank you for the help!

#### R.M.

##### Junior Member
For part A, start with a simpler question: for one applicant, probability that it is a nurse. Now if you have that scenario five times, what do you to the probabilities?

#### JeffM

##### Elite Member
Because we have no clue what is in that module, how can we possibly tell you how to solve these problems if you “follow only the contents of the module”?

You have not said anything about the probabilities that relate to those types of event.

It possibly looked something like this.

Union of events a and b. P(a or b) = P(a) + P(b) - P(a and b)

Intersection event of events a and b. P(a and b) = P(a given b) * P(b) if P(b) > 0.

Mutually exclusive events a and b. P(a and b) = 0, which implies P(a or b) = P(a) + P(b).

Now that is very useful information, but if that is ALL you have learned about probability, these problems are totally beyond you.

Perhaps, however, you have learned other things about probabilities, either in this or in an EARLIER module.

If you are asking what is the relevance of of this module to answering this problem, that we can answer.

There are six possible events. 5 nurses and no radiologists. 4 nurses and 1 radiologist. 3 nurses and 2 radiologists, 2 nurses and 3 radiologists. 1 nurse and 4 radiologists. No nurse and 5 radiologists.

Now consider the event “at least three nurses.“ Is it not obvious that this is a union event of three nurses, four nurses, and five nurses? Is it not also obvious that those three individual probabilities are mutually exclusive? So you should be able to calculate the probability of the union if you can calculate the individual probabilities of 3, 4, or 5 nurses.