There has been an outbreak of whooping cough in America. Though still rare, one
ID: 3358050 • Letter: T
Question
There has been an outbreak of whooping cough in America. Though still rare, one study found that 1 in 10,000 children turned out to have whooping cough. There is a screening for whooping cough that correctly diagnoses the disease in 99% of children who have it, and correctly diagnoses its absence in 98% of children who don’t have it. a. Find the probability that a child has whooping cough AND gets a positive test result. b. Find the probability that a child does not have whooping cough AND gets a negative test result. c. Find the probability that a child does not have whooping cough AND gets a positive test result. d. Find the probability that a child does have whooping cough AND gets a negative test result. e. Find the probability that a child will test positive. f. Find the probability that a child has whooping cough, given that the child tested positive. g. Find the probability that a child does not have whooping cough, given that the child tested positive. h. Is the test reliable? Why or why not?
Explanation / Answer
A - has whooping cough
B- test positive
P(A) = 1/10000
P(B|A) = 0.99
P(B'|A') = 0.98
a. Find the probability that a child has whooping cough AND gets a positive test result.
=P(B and A) = P(B|A) * P(A) = 0.99*1/10000 = 0.000099
b. Find the probability that a child does not have whooping cough AND gets a negative test result.
= P(B' and A') = P(B'|A') * P(A') = 0.98 * (1 - 1/10000) = 0.979902
c. Find the probability that a child does not have whooping cough AND gets a positive test result.
= P(B and A') = P(B|A') * P(A') = ( 1 - 0.98) * (1- 1/10000)= 0.019998
d. Find the probability that a child does have whooping cough AND gets a negative test result.
= P(A and B') = P(B'|A) P(A) = (1 - 0.99) * 1/10000 = 0.000001
e) P(B) = 0.000099+ 0.019998 = 0.020097
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