Question

1. medical specialities the following doctors were ob - served on staff at a local hospital. choose one doctor at random; what is the probability that a. she is a pathologist? b. he is an orthopedist or an md?

Explanation:

Step1: Compute total number of doctors

Total doctors \(=6 + 1+7 + 2+20 + 2=38\)

Step2: Solve part (a)

Number of pathologists \(=6 + 1=7\)
Probability \(P(\text{pathologist})=\frac{7}{38}\)

Step3: Solve part (b)

Number of orthopedists \(=20 + 2=22\)
Number of MDs \(=6 + 7+20=33\)
Number of orthopedists who are MDs \(=20\)
Using the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)
\(P(\text{orthopedist or MD})=\frac{22}{38}+\frac{33}{38}-\frac{20}{38}=\frac{22 + 33-20}{38}=\frac{35}{38}\)

Answer:

a. \(\frac{7}{38}\)
b. \(\frac{35}{38}\)