A First Course in Probability (10th Edition)
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ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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The Samsung plant in Newberry is an assembly plant for home appliances. They assembly three types of appliances including washing machine, dishwasher, and oven (reference by W, R, and O). Each type of appliance is produced in a different assembly line which has some amount of output per day. Let’s imagine a quality engineer has gathered the following data in Table 1 from a small period of production, counting the number of products with defects and without defects. Let D indicates a defective product and ND indicates not defective.
Washing Machine Dishwasher Oven:
Defective
5
2
15
Not defective
63
86
45
Table 1: Number of products with and without defects by type
a. Overall, what is the probability that a randomly selected product is defective?
b. What is the probability that a randomly selected product is an oven?
c. What is the probability that a product is defective, given it is an oven?
d. What is the probability that a product is defective, given it is either an oven or a dishwasher?
e. What is the probability that a product is either an oven or a dishwasher given it is defective?
Let’s imagine that all the defective products are dumped in a recycling bin. A person randomly selects a product from the recycling bin.
f. What is the probability that this randomly selected product in the recycling bin is a washing machine?
g. What is the probability that this randomly selected product in the recycling bin is dishwasher?
h. What is the probability that a product is defective AND is an oven?
i. Are the events “defective product” and “being an oven” independent or not? You must justify your answer!
j. Are the events “defective product” and “being an oven” mutually exclusive or not? You must justify your answer!
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