Suppose that 8
out of the 23
doctors in a small hospital are General Practitioners, 7
out of the 23
are under the age of 50
, and 2
are both General Practitioners and under the age of 50
. What is the probability that you are randomly assigned a General Practitioner or a doctor under the age of 50
? Enter a fraction or round your answer to 4
decimal places, if necessary.
First, let's calculate the total number of doctors who are either General Practitioners or under the age of 50.
Total General Practitioners = 8
Total doctors under the age of 50 = 7
Doctors who are both General Practitioners and under the age of 50 = 2
Total doctors who are either General Practitioners or under the age of 50:
Total = General Practitioners + doctors under the age of 50 - both = 8 + 7 - 2 = 13
Now, to calculate the probability of randomly selecting a doctor who is either a General Practitioner or under the age of 50, we divide the total number of favorable outcomes by the total number of possible outcomes:
P(General Practitioner or under age of 50) = Total doctors who are either General Practitioners or under the age of 50 / Total number of doctors
P(General Practitioner or under age of 50) = 13 / 23 ≈ 0.5652
Therefore, the probability that you are randomly assigned a General Practitioner or a doctor under the age of 50 is approximately 0.5652.