An inner tube manufacturer makes two styles regular and ultr

An inner tube manufacturer makes two styles: regular and ultralight. Regular tubes account for 80% of sales, and ultralight tubes account for 20%. Defects in the tubes happen sometimes, and 10% of the regular tubes and 18% of the ultralight tubes are defective. If an inner tube is selected at random, what is the probability that it will be defective? Express as a decimal.

Solution

P(regular) = 80%

P(ultralight) = 20%

P(defective | regular) = 10%

P(defective | unltralight) = 18%

Lets assume that in all 1000 tubes were sold

So, regular = 80% of 1000 = 800

ultralight = 20% of 1000 = 200

Defective regular = 10% of 800 = 0.1*800 = 80

Defective ultralight = 18% of 200 = 0.18 * 200 = 36

P(defective) = (80 + 36) / 1000 = 116/1000 = 0.116

Answer ----> 0.116