Question

An underwriter is analyzing the heights of his clients. He categorizes 35% as tall, 40% as medium height, and 25% as short. He then randomly picks two clients (from his very large client base). What is the probability that neither is tall and at most one is medium height

Answer 1

Answer:

0.2625 = 26.25% probability that neither is tall and at most one is medium height.

Step-by-step explanation:

Desired outcomes:

Short - Short

Short - Medium

Medium - Short

Probability of two short:

25% are short, so:

$P(A) = (0.25)^2 = 0.0625$

Probability of short medium or medium short

25% short, 40% medium. So

$P(B) = 2*0.25*0.4 = 0.2$

What is the probability that neither is tall and at most one is medium height?

$P = P(A) + P(B) = 0.0625 + 0.2 = 0.2625$

0.2625 = 26.25% probability that neither is tall and at most one is medium height.