Respuesta :
Answer:
0.6957 = 69.57% probability that you are randomly assigned a General Practitioner or a doctor under the age of 50.
Step-by-step explanation:
I am going to solve this question treating these events as Venn events.
I am going to say that:
Event A: General practitioner.
Event B: Under the age of 50.
Suppose that 9 out of the 23 doctors in a small hospital are General Practitioners
This means that [tex]P(A) = \frac{9}{23}[/tex]
10 out of the 23 are under the age of 50
This means that [tex]P(B) = \frac{10}{23}[/tex]
3 are both General Practitioners and under the age of 50.
This means that [tex]P(A \cap B) = \frac{3}{23}[/tex]
What is the probability that you are randomly assigned a General Practitioner or a doctor under the age of 50?
This is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Considering the values we have for this exercise.
[tex]P(A \cup B) = \frac{9}{23} + \frac{10}{23} - \frac{3}{23} = \frac{9+10-3}{23} = \frac{16}{23} = 0.6957[/tex]
0.6957 = 69.57% probability that you are randomly assigned a General Practitioner or a doctor under the age of 50.
