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A new test for strep throat is developed. 500 children with sore throat are tested with the new test and also have throat cultures taken. Assume that the throat cultures are 100% accurate in determining whether or not a child has a strep infection.
The following data are collected:
The new test showed positive results (strep throat) in 210 children out of the 276 children who had positive strep cultures
The new test showed negative results (no strep throat) in 190 children out of 224 children who had negative strep cultures.
If the prevalence (pre-test probability) of strep throat among children in the population is 2%, what is the probability that a child has strep throat if the new test result for that child is positive? (Hint: This is a problem using Bayes' Theorem).
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