Question

a person wants to purchase a dvd drive for his laptop computer. assume that 60% of the drives are made outside the united states. of the u.s - made drives, 4% are defective and of the foreign - made drives, 8% are defective. determine the probability that the drive purchased is u.s. made and is not defective.
the probability is
(type an integer or decimal rounded to four decimal places as needed.)

Explanation:

Step1: Calculate the proportion of U.S - made drives

Since 60% of the drives are made outside the US, the proportion of U.S - made drives is \(1 - 0.6=0.4\)

Step2: Calculate the proportion of non - defective U.S - made drives

The proportion of defective U.S - made drives is 4% or 0.04. So the proportion of non - defective U.S - made drives is \(1 - 0.04 = 0.96\)

Step3: Calculate the probability of a U.S - made non - defective drive

Using the multiplication rule for independent events (if \(A\) is the event of a drive being U.S - made and \(B\) is the event of a drive being non - defective, \(P(A\cap B)=P(A)\times P(B|A)\)), we have \(P = 0.4\times0.96\)

$$P=0.4\times0.96 = 0.384$$

Answer:

\(0.3840\)