Suppose that 9
out of the 23
doctors in a small hospital are General Practitioners, 7
out of the 23
are under the age of 45
, and 5
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 4
decimal places, if necessary.
First, let's find the probability of being assigned a General Practitioner or a doctor under the age of 45.
Total number of doctors = 23
Number of General Practitioners = 9
Number of doctors under the age of 45 = 7
Number of doctors who are both General Practitioners and under the age of 45 = 5
Using the principle of inclusion-exclusion:
P(General Practitioner or under 45) = P(General Practitioner) + P(Under 45) - P(General Practitioner and Under 45)
P(GP or under 45) = (9/23) + (7/23) - (5/23)
P(GP or under 45) = 11/23
Therefore, the probability of being randomly assigned a General Practitioner or a doctor under the age of 45 is 11/23 or approximately 0.4783.