Question

Suppose that 7out of the 19 doctors in a small hospital are General Practitioners, 8 out of the 19 are under the age of 45, and 2 are both General Practitioners and under the age of 45. What is the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45? Enter a fraction or round your answer to four decimal places if necessary

Answer 1

To answer this question we will use the following expression to compute the probability that an event occurs:

`(FavorableOutcomes)/(TotalOutcomes).`

Therefore:

`\begin{gathered} P(Practitioner)=(7)/(19), \\ P(Under45)=(8)/(19), \\ P(Practitioner\text{ and }Under45)=(2)/(19). \end{gathered}`

Now, recall that:

`P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B).`

Therefore:

`\begin{gathered} P(Practitioner\text{ or }Under45)=P(Practitioner)+P(Under45)- \\ P(Practitioner\text{ and }Under45). \end{gathered}`

Substituting

`\begin{gathered} P(Practitioner)=(7)/(19), \\ P(Under45)=(8)/(19), \\ P(Practitioner\text{ and }Under45)=(2)/(19), \end{gathered}`

in the above equation we get:

`P(Practitioner\text{ or }Under45)=(7)/(19)+(8)/(19)-(2)/(19).`

Simplifying the above result we get:

`P(Practitioner\text{ or Under}45)=(13)/(19).`

Answer:

`(13)/(19).`