Question

In a hospital ward, there are 12 nurses and 4 doctors. 3 of the nurses and 2 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? @IMStuck @TheSaint905621 @Compassionate @phi @math&ing001 @acxbox22

Answer 1

@TSwizzle @TheSaint905621

Answer 2

11/16

Answer 3

\[P(\text{female or doctor})=P(\text{female})+P(\text{doctor})-P(\text{female and doctor})\]
There's a total of 11 females (9 nurses, 2 doctors) in the group of 16, and there are 4 doctors. Two of these doctors are also female, so
\[P(\text{female or doctor})=\frac{11}{16}+\frac{4}{16}-\frac{2}{16}\]