A company has invented a new device that turns red when exposed to an injured pitcher. The company claims that the device predicts pitcher injuries with 90% accuracy

"A company has invented a new device that turns red when exposed to an injured pitcher. The company claims that the device predicts pitcher injuries with 90% accuracy -- given that a pitcher is actually injured, the device will turn red 90% of the time. Given that the pitcher is not injured, the device will turn red 20% of the time. Assume that the population-level injury risk for pitchers is 5%. A randomly selected player takes the test and the device turns red. What is the probability that he is injured?"

Use the Table Method to answer this question. Fill in all cells of the table, not just the ones you need for the appropriate calculation. Sanity check: a little above 19%. Do your work by hand on paper (or in Excel), take a picture with your phone (or screenshot), then after knitting insert that picture into your Word document.

Expert Solution

P( pitcher injured ) = 0.05
P( pitcher is not injured ) = 0.95

P( red | pitcher injured)= 0.9
P( red | pitcher is not injured)= 0.2

P(red) = P(pitcher injured) * P(red| pitcher injured) + P(pitcher is not injured) *P(red| pitcher is not injured) + P( )*P(red| ) = 0.05*0.9+0.95*0.2+*= 0.235

P(pitcher injured| red) = P(pitcher injured)*P(red| pitcher injured)/P(red)= 0.05*0.9/0.235= 0.045/0.235 = 0.1915

	red	not red	total
pitcher injured	0.045	0.005	0.05
pitcher is not injured	0.19	0.76	0.95
total	0.235	0.765	1

orchestra answered 2 years ago

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