Question

Two factories I and II produce phones for brand ABC. Factory I produces 60% of all ABC phones, and factory II produces 40%. 10% of phones produced by factory I are defective, and 20% of those produced by factory II are defective. You purchase a brand ABC phone, and assume this phone is randomly chosen from all ABC phones. Suppose the phone is not defective. What is the probability that it came from factory II?

Answer 1

Answer:

0.3721 or 37.21%

Step-by-step explanation:

P(I) = 0.60; P(II) = 0.40;

P(not defective I) = 0.90; P(not defective II) = 0.80

The probability that the phone came from factory II, given that is not defective, is determined by the probability of a phone from factory II not being defective divided by the probability of a phone not being defective.

$P(II|not) = \frac{P(II)*P(not_{II})}{P(II)*P(not_{II})+P(I)*P(not_{I})}\\P(II|not) = \frac{0.40*0.80}{0.40*0.80+0.60*0.90}\\ P(II|not) =0.3721 = 37.21\%$

The probability is 0.3721 or 37.21%.