At WSU hospital, 64% of patients have water on the knee, 45% have butterflies in the stomach, and 20% have both conditions. What is the probability that a random patient has neither condition? What is the probability that a random patient has exactly one of the two conditions?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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At WSU hospital, 64% of patients have water on the knee, 45% have butterflies in the stomach, and 20% have both conditions. What is the probability that a random patient has neither condition? What is the probability that a random patient has exactly one of the two
conditions?

Expert Solution
Step 1

Given:

suppose 

A = patient is having water on the knee PA=0.45

B = patients are having butterflies in the stomach PB=0.20

PAB=0.20

Step 2

Calculation:

the probability that an arbitrary patient has neither condition =PABc

 

PABc=1-PAB=1-{PA+PB-PAB}=1-{0.64+0.45-0.20}=1-0.89=0.11

Required Probability is 0.11

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