Answer to Question #350585 in Statistics and Probability for sergu

Question

1.      In a hospital unit, there are 8 nurses and 5 physicians; 7 nurses and 3 physicians are females. In a staff person is selected, find the probability that the subject is nurse or male.

 

Staff                     females               males                   total

Nurse                        7                          1                         8

Physicians                3                         2                         5

                                  10                          3                        13

Answer 1

$A=\{\text{The selected subject is nurse}\}$

$B=\{\text{The selected subject is male}\}$

$AB=\{\text{The selected subject is nurse and male}\}$

$A\cup B=\{\text{The selected subject is nurse or male}\}$

$|\Omega|=13$, $|A|=8$, $|B|=3$, $|AB|=1$.

$\mathbb{P}(A)=\frac{|A|}{|\Omega|}=\frac{8}{13}$

$\mathbb{P}(B)=\frac{|B|}{|\Omega|}=\frac{3}{13}$

$\mathbb{P}(AB)=\frac{|AB|}{|\Omega|}=\frac{1}{13}$

By the probability addition theorem $\mathbb{P}(A\cup B)=\mathbb{P}(A)+\mathbb{P}(B)-\mathbb{P}(AB)$.

$\mathbb{P}(A\cup B)=\frac{8}{13}+\frac{3}{13}-\frac{1}{13}=\frac{8+3-1}{13}=\frac{10}{13}$