solve these question please......!

Question

A company produces batteries. On average, 85% of all batteries produced are good. Each

battery is tested before being dispatched, and the inspector correctly classifies the battery 90%

of the time.

A.) What percentage of the batteries will be “classified as good”?

B.)What is the probability that a battery is defective given that it was classified as good?

Answer 1

85% of the batteries are good and 15% are bad. to find part A, split this into two groups: 1) the batteries that are good and correctly classified as good, 2) the batteries that are bad but are incorrectly classified as good. To do that, you would multiply P(good)*P(correct) + P(bad)*P(incorrect) = 0.85*0.9+0.15*0.1 = 0.78.

for part B: P(defective | classified as good) = P(defective and classified as good)/P(classified as good) = 0.15*0.1/0.78 = 0.1923