Question

The Institute of Infrequent Afflictions (IIA) says that cat flu is a rare disease that afflicts 1.6% of the US population. The institute developed a test to detect this disease in the human body and a clinical trial was conducted. 1% of the subjects who had cat flu were identified incorrectly by the test. 2.5% of the subjects did not have the cat flu were identified incorrectly by the test Write down the six probabilities that this question gives us. 1. Type in the 6 equations. Use mathematical notation. For example P(A/B) = 0.12. You do not need to do any other calculations. Next type in the answer to the following question. 2. If a random person goes in for a test, what is the probability that he will tests positive? HEML Editong

Answer 1

0.984 0.016 had cat flu do not have cat flu 0.99 0.01 0.975 0.025 identified correctly identified incorrectly identified correctly identified incorrectly

Let A be the event having cat flu

B be the event being identified correctly.

$P(A)=0.016$

$P(A^c)=0.984$

$P(B\mid A)=0.99$

$P(B^c\mid A)=0.01$

$P(B\mid A^c)=0.975$

$P(B^c\mid A^c)=0.025$

2) The probability he will test positive

=

= 0.016 +0.99 +0.984 +0.025 = 0.0404