Question

In a hospital ward, there are 10 nurses and 6 doctors. 4 of the nurses and 3 of the doctors are male. If a person is randomly selected from this group, what is the probability that the person is female or a doctor?

Answer 1

`3/4`

Though, that's based on the false assumption that gender is binary. Let your math teacher have it for that.

Explanation:

In a probability problem that uses the conjunction "or," you'll need to add the probabilities of mutually exclusive results. There are 16 people in the ward.

First, you can find the probability of selecting a doctor. There are 6 doctors, so the probability is `6/16`.

Then, you need to add the probability of selecting a female minus the probability of selecting a female doctor (as you've already covered this with doctors). If there were only two genders, then the 6 nurses who are not male would be the only females who aren't doctors.

So, the probability of selecting a female or doctor is `(6 + 6) / 16`, or `12/16`.

This can be reduced to `3/4` or `75%`.