Question #350585

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


1
Expert's answer
2022-06-15T05:49:50-0400

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

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

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

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


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


P(A)=AΩ=813\mathbb{P}(A)=\frac{|A|}{|\Omega|}=\frac{8}{13}

P(B)=BΩ=313\mathbb{P}(B)=\frac{|B|}{|\Omega|}=\frac{3}{13}

P(AB)=ABΩ=113\mathbb{P}(AB)=\frac{|AB|}{|\Omega|}=\frac{1}{13}


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


P(AB)=813+313113=8+3113=1013\mathbb{P}(A\cup B)=\frac{8}{13}+\frac{3}{13}-\frac{1}{13}=\frac{8+3-1}{13}=\frac{10}{13}

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