Question

In: Statistics and Probability

Put each problem on a separate worksheet in an Excel file. Type the tabular data into...

Put each problem on a separate worksheet in an Excel file. Type the tabular data into the spreadsheet
Make Excel do all of the necessary calculations
Report answers on the worksheet
Label answers as the questions are labelled: a, b, c,…
Use the probability notation p(A), p(Aand B),… etc

2. A manufacturing firm in Pittsburgh, Pennsylvania receives shipments of part from two suppliers (we’ll call them A1 and A2. The probability that the parts come from A1 is 0.65, the probability that they come from A2 is 0.35.

Past experience has shown that if the parts came from A1, the probability that they are good is 0.98. If the parts came from A2, the probability that they are good is 0.95.

a. Draw the probability tree

b. What is the probability that a part came from A1 and is good?

c. What is the probability that a part came from A2 and is bad?

d. Using the information given and your results from b and c complete the contingency table below


	Supplier A1	Supplier A2
Good part
Bad part

e. What is the probability that a randomly selected part is bad?

f. A randomly selected part has been found to be bad. What is the probability that is from Supplier A1?

g. A randomly selected part has been found to be bad. hat is the probability that is from Supplier A2?

Expert Solution

Solution:

Given:

P(A1) = 0.65

P(A2) = 0.35

if the parts came from A1, the probability that they are good is 0.98.

That is: P(Good | A1) = 0.98

If the parts came from A2, the probability that they are good is 0.95.

P( Good | A2) = 0.95

Part a. Draw the probability tree

Part b. What is the probability that a part came from A1 and is good?

P(A1 and Good) = P( Good | A1) x P(A1)

P(A1 and Good) = 0.98 x 0.65

P(A1 and Good) = 0.637

Part c. What is the probability that a part came from A2 and is bad?

P( A2 and Bad) = P( Bad | A2 ) x P(A2)

P( A2 and Bad) = 0.05 x 0.35

P( A2 and Bad) = 0.0175

Part d. Using the information given and your results from b and c complete the contingency table below

	Supplier A1	Supplier A2
Good part	0.637	0.3325	P(Good) = 0.9695
Bad part	0.013	0.0175	P(Bad) = 0.0305
	0.65	0.35	1

Part e. What is the probability that a randomly selected part is bad?

P(Bad) =0.013 + 0.0175

P(Bad) = 0.0305

Part f. A randomly selected part has been found to be bad. What is the probability that is from Supplier A1?

P(A1 | Bad) =............?

From table , we have:

P(A1 and Bad) = 0.013

and P(Bad) = 0.0305

Thus

Part g. A randomly selected part has been found to be bad. What is the probability that is from Supplier A2?

P(A2 | Bad) = .........?

orchestra answered 1 year ago

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