In a hospital ward, there are 16 nurses and 5 doctors. 3 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 male or a doctor?

1 Answer
EZ as pi
Jul 20, 2016

#P("male or doctor") =8/21#

Explanation:

In this question, the outcomes are not mutually exclusive, meaning that one does not exclude the others. It is possible for someone to belong to both categories given.

"OR" implies that the Probabilities have to be added.
"AND" implies that they should be multiplied.

#P("male or doctor") = P("male") + P("doctor") - P("both")#

#P("male or doctor") =6/21 + 5/21- 3/21 = 8/21#

If we do not subtract the people who are male and doctors, they will be counted twice.

#P("male or doctor") =8/21#

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