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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

Respuesta :

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

[tex]\frac{FavorableOutcomes}{TotalOutcomes}.[/tex]

Therefore:

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

Now, recall that:

[tex]P(A\text{ or }B)=P(A)+P(B)-P(A\text{ and }B).[/tex]

Therefore:

[tex]\begin{gathered} P(Practitioner\text{ or }Under45)=P(Practitioner)+P(Under45)- \\ P(Practitioner\text{ and }Under45). \end{gathered}[/tex]

Substituting

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

in the above equation we get:

[tex]P(Practitioner\text{ or }Under45)=\frac{7}{19}+\frac{8}{19}-\frac{2}{19}.[/tex]

Simplifying the above result we get:

[tex]P(Practitioner\text{ or Under}45)=\frac{13}{19}.[/tex]

Answer:

[tex]\frac{13}{19}.[/tex]

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