Question

2. How many ways can you select a planning committee of three for a group of eight executives

3. You have produced four advertisements to use while selling a new product. What are all the possible ways you can order these four ads if you plan to only use two during the summer months

4. A manufacturer of cranes purchases electric motors from three suppliers: General Electric, Westinghouse, and Samsung. Thirty percent of the motors are purchased from General Electric, 20% from Westinghouse and 50% from Samsung. The crane manufacturer has history on each company and knows that 3% of the motors from General Electric will be defective 5% from Westinghouse and 4% from Samsung. When the crane manufacturer receives the motors they are warehoused without identifying the supplier. A worker selects a motor for installation and finds it defective. What is the probability that the motor came from Westinghouse? (Show your work)

5. On an average day 2.5% of the people walking down your street purchase coffee from your beverage stand. You read an article suggesting the number of people choosing to drink coffee doubts when the outside temperature drops below 50 degrees. You quickly find that 75 out of 365 days have a temperature of 50 degrees or below. Use the new information to the population the table below. Let P(A1) be the probability of a rainy day. (Show your work)

(1)	(2)	(3)	(4)	(5)
Events	Prior Probabilities	ConditionalProbabilities	Joint Probabilities	Posterior Probabilities
Ai	P(Ai)	P(B|Ai)	P(Ai I B)	P(Ai |B)
A1
A2		1.00
			P(B) = .025	1.0000

Answer 1

2:

Here order of selection does not matter so number of possible planning committees is

4:

Let G shows the event that motors came from General Electric, W shows the event that motors cam from Westinghouse and S shows the event that motors came from Samsung. So we have

P(G) = 0.30, P(W) = 0.20, P(S) = 0.50

Let D shows the event that motor is defective. So

P(D|G) = 0.03, P(D|W) = 0.05, P(D|S) = 0.04

By the Baye's theorem the probability that the motor came from Westinghouse given that it is defective is

P(W|D) = [ P(D|W)P(W) ] / [ P(D|G)P(G)+P(D|W)P(W)+P(D|S)P(S)] = [ 0.05 * 0.20] / [ 0.03*0.30 + 0.05*0.20 + 0.04 * 0.50] = 0.2564

Answer: 0.2564