3. One month of doctors office visits are used to determine the following percen

Question

3. One month of doctors office visits are used to determine the following percentages: 25% of patients had headaches and 40% had the flu. One of the patients is selected at random. Let H represent the event the (a) [1 point] Given the information above, what are the smallest and largest values P(H n F can be (b) You are also told that if a patient did NOT have a headache, then the probability of the patient having patient had a headache, and let F represent the even the person had patient had the flu. Explain your reasoning. the flu was 40%. Use this additional information to determine the following, showing all of your loge and steps in a clear fashion i. [1.25 point) P(F n ) ii. [2 points] P(Fn H) ii 1.25 point] P(F U H) iv. [2 points] Are the events F and H ndependent? Explain why or why not

Explanation / Answer

a)as P(H)+P(F)=0.25+0.40 =0.75 which is less than 1 ; theefore

here smallest value of P(H n F) =max(0 ,P(H)+P(F)-1) =max(0,-0.25) =0

largest value of P(H n F)=min(P(H),P(F)) =min(0.25 ,0.40)= 0.25

b)

here P(F|Hc) =0.40

i) P(F n Hc) =P(Hc)*P(F|Hc) =(1-0.25)*0.40=0.30

ii) P(F n H)=P(F)-P(Fn Hc) =0.40-0.30=0.10

iii)P(F u H) =P(F)+P(H)-P(F n H)=0.25+0.40-0.10=0.55

iv)as P(F n H) =P(F)*P(H) ; therefore F and H are independent

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