I'm unsure of the following questions, but I attempted them and posted my answers. If anyone could verify if I'm on the right track, I'd appreciate it!
A company uses three different assembly lines -
A1, A2, and A3 - to manufacture a particular component. Of those manufactured by A1,
5% need rework to remedy a defect, whereas 8% of A2's components and 10% of A3's components need rework. Suppose that 50% of all components are produced by A1, whereas 30% are produced by A2 and 20% come from A3.
(a) What is the probability that a randomly selected component comes
from A1 and needs rework?
(b) What is the probability that a randomly selected component needs
rework?
My answers:
(a) (0.05)(0.5) = 0.025
(b) 1 - (0.95)(0.92)(0.9) = 0.2134
Suppose a new Internet company Mumble.com was to require all employees to take a drug test. Mumble.com can afford only the inexpensive drug test - the one with a 5% false positive and a 10% false negative rate. (That means that five percent of those who are not using drugs will incorrectly test positive, and ten percent of those who are actually using drugs will test negative.) Suppose that 10% of those who work for Mumble.com are using the drugs for which Mumble.com is checking. An employee is chosen at random.
(a) What is the probability the employee both uses drugs and tests positive?
(b) What is the probability the employee does not use drugs but tests
positive anyway?
(c) What is the probability the employee tests positive?
(d) If the employee has tested positive, what is the probability he or she
uses drugs?
My answers:
(a) (0.1)(1-0.1) = 0.09
(b) (1-0.1)(0.05) = 0.045
(c) (0.9)(0.05) + (0.1)(0.9) = 0.135
(d) ((0.1)(0.9)) / 0.135 = 0.67