Questions: Suppose that 4 out of the 19 doctors in a small hospital are General Practitioners, 8 out of the 19 are under the age of 40, and 2 are both General Practitioners and under the age of 40. What is the probability that you are randomly assigned a General Practitioner or a doctor under the age of 40? Enter a fraction or round your answer to 4 decimal places, if necessary.

$Suppose that 4 out of the 19 doctors in a small hospital are General Practitioners, 8 out of the 19 are under the age of 40, and 2 are both General Practitioners and under the age of 40. What is the probability that you are randomly assigned a General Practitioner or a doctor under the age of 40? Enter a fraction or round your answer to 4 decimal places, if necessary.$

Transcript text: Suppose that 4 out of the 19 doctors in a small hospital are General Practitioners, 8 out of the 19 are under the age of 40, and 2 are both General Practitioners and under the age of 40. What is the probability that you are randomly assigned a General Practitioner or a doctor under the age of 40? Enter a fraction or round your answer to 4 decimal places, if necessary.

Solution

Solution Steps

Step 1: Calculate the probability of being assigned to a General Practitioner

Using the formula $P(G) = \frac{G}{N}$, where $G = 4$ and $N = 19$, we get $P(G) = 0.211$.

Step 2: Calculate the probability of being assigned to a doctor under the specified age

Using the formula $P(A) = \frac{A}{N}$, where $A = 8$ and $N = 19$, we get $P(A) = 0.421$.

Step 3: Calculate the probability of being assigned to a doctor who is both a General Practitioner and under the specified age

Using the formula $P(B) = \frac{B}{N}$, where $B = 2$ and $N = 19$, we get $P(B) = 0.105$.

Step 4: Use the principle of inclusion-exclusion to find the probability of being assigned to a General Practitioner or a doctor under the specified age

Using the formula $P(G \cup A) = P(G) + P(A) - P(B)$, we get $P(G \cup A) = 0.211 + 0.421 - 0.105 = 0.526$.