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In-a-hospital-unit-there-are-8-nurses-and-5-physicians-7-of-them-are-female-nurses-and-3-of-them-are-male-physicians-what-is-the-the-probability-of-selecting-a-staff-who-is-Nurse-or-Male-plzz-help-




Question Number 48553 by Cheyboy last updated on 25/Nov/18
In a hospital unit,there are 8 nurses  and 5 physicians. 7 of them are  female nurses and 3 of them are  male physicians.  what is the the probability of  selecting a staff who is Nurse or  Male?  plzz help
$$\mathrm{In}\:\mathrm{a}\:\mathrm{hospital}\:\mathrm{unit},\mathrm{there}\:\mathrm{are}\:\mathrm{8}\:\mathrm{nurses} \\ $$$$\mathrm{and}\:\mathrm{5}\:\mathrm{physicians}.\:\mathrm{7}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are} \\ $$$$\mathrm{female}\:\mathrm{nurses}\:\mathrm{and}\:\mathrm{3}\:\mathrm{of}\:\mathrm{them}\:\mathrm{are} \\ $$$$\mathrm{male}\:\mathrm{physicians}. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of} \\ $$$$\mathrm{selecting}\:\mathrm{a}\:\mathrm{staff}\:\mathrm{who}\:\mathrm{is}\:\mathrm{Nurse}\:\mathrm{or} \\ $$$$\mathrm{Male}? \\ $$$$\mathrm{plzz}\:\mathrm{help} \\ $$$$ \\ $$$$ \\ $$
Commented by mr W last updated on 26/Nov/18
MJS sir:  what if 6 of them are female and 4  of them are male physicians?  is the probability ((14)/(13))>1 ?
$${MJS}\:{sir}: \\ $$$${what}\:{if}\:\mathrm{6}\:{of}\:{them}\:{are}\:{female}\:{and}\:\mathrm{4} \\ $$$${of}\:{them}\:{are}\:{male}\:{physicians}? \\ $$$${is}\:{the}\:{probability}\:\frac{\mathrm{14}}{\mathrm{13}}>\mathrm{1}\:? \\ $$
Commented by MJS last updated on 26/Nov/18
8 nurses       7 female ⇒ 1 male  5 physicians       3 male ⇒ 2 female  ⇒ probabikity ((11)/(12))  sorry for mistake yesterday      8 nurses + 5 physicians       6 female ⇒ 7 male  5 physicians       4 male ⇒ 1 female  ⇒ 8 nurses             5 female ⇒ 3 male  probability in this case ((12)/(13)) because we must  count all nurses anyway, plus only male physicians
$$\mathrm{8}\:\mathrm{nurses} \\ $$$$\:\:\:\:\:\mathrm{7}\:\mathrm{female}\:\Rightarrow\:\mathrm{1}\:\mathrm{male} \\ $$$$\mathrm{5}\:\mathrm{physicians} \\ $$$$\:\:\:\:\:\mathrm{3}\:\mathrm{male}\:\Rightarrow\:\mathrm{2}\:\mathrm{female} \\ $$$$\Rightarrow\:\mathrm{probabikity}\:\frac{\mathrm{11}}{\mathrm{12}} \\ $$$$\mathrm{sorry}\:\mathrm{for}\:\mathrm{mistake}\:\mathrm{yesterday} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{8}\:\mathrm{nurses}\:+\:\mathrm{5}\:\mathrm{physicians} \\ $$$$\:\:\:\:\:\mathrm{6}\:\mathrm{female}\:\Rightarrow\:\mathrm{7}\:\mathrm{male} \\ $$$$\mathrm{5}\:\mathrm{physicians} \\ $$$$\:\:\:\:\:\mathrm{4}\:\mathrm{male}\:\Rightarrow\:\mathrm{1}\:\mathrm{female} \\ $$$$\Rightarrow\:\mathrm{8}\:\mathrm{nurses} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}\:\mathrm{female}\:\Rightarrow\:\mathrm{3}\:\mathrm{male} \\ $$$$\mathrm{probability}\:\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\frac{\mathrm{12}}{\mathrm{13}}\:\mathrm{because}\:\mathrm{we}\:\mathrm{must} \\ $$$$\mathrm{count}\:\mathrm{all}\:\mathrm{nurses}\:\mathrm{anyway},\:\mathrm{plus}\:\mathrm{only}\:\mathrm{male}\:\mathrm{physicians} \\ $$
Answered by MJS last updated on 26/Nov/18
8 nurses out of 13 people  4 male out of 13 people  but 1 person in both sets  ⇒ 11 persons are “nurse or male”  ⇒ p=((11)/(13))
$$\mathrm{8}\:\mathrm{nurses}\:\mathrm{out}\:\mathrm{of}\:\mathrm{13}\:\mathrm{people} \\ $$$$\mathrm{4}\:\mathrm{male}\:\mathrm{out}\:\mathrm{of}\:\mathrm{13}\:\mathrm{people} \\ $$$$\mathrm{but}\:\mathrm{1}\:\mathrm{person}\:\mathrm{in}\:\mathrm{both}\:\mathrm{sets} \\ $$$$\Rightarrow\:\mathrm{11}\:\mathrm{persons}\:\mathrm{are}\:“\mathrm{nurse}\:{or}\:\mathrm{male}'' \\ $$$$\Rightarrow\:{p}=\frac{\mathrm{11}}{\mathrm{13}} \\ $$
Commented by Cheyboy last updated on 25/Nov/18
Thank you sir
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{sir} \\ $$

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