Question

In: Statistics and Probability

A company has two machines that produce widgets. The new machine produces 75% widgets and the...

A company has two machines that produce widgets. The new machine produces 75% widgets and the older machine produces 25% widgets. Further, the new machine produces 10% defective widgets, while the older machine produces 30% defective widgets. If a widget is randomly selected what is the probability that it is defective?

Expert Solution

A company has two machines that produce widgets. The new machine produces 75% widgets and the old one produces 25% widgets.

The new machine produces 10% defective widgets, and the old machine produces 30% defective widgets.

So, given that

P(A randomly selected widget is produced by new machine)=75/100=0.75

P(A randomly selected widget is produced by old machine)=25/100=0.25

P(widget is defective|produced by new machine)=10/100=0.10

P(widget is defective|produced by old machine)=30/100=0.30

To find the chance that a randomly slected machine is defective.

So, we have to find

P(A randomly selcted machine is defective)

=P(A machine is defective and produced by old machine)+P(A machine is defective and produced by new machine)

From conditional probability, we know that P(A and B)=P(A)P(B|A).

Now, by total probability theorem, this becomes

=[P(widget is produced by new machine)*P(widget is defective|produced by new machine)]+[P(widget is produced by old machine)*P(widget is defective|produced by old machine)]

=0.75*0.10+0.25*0.30

=0.075+0.075

=0.150.

So, the probability that a randomly selected machine is defective is 0.150.

orchestra answered 1 year ago

A supervisor needs to produce widgets. Two machines are able to make the widgets. Machine A...

A supervisor needs to produce widgets. Two machines are able to make the widgets. Machine A takes 2 hours to set up and can then make widgets at a rate of 80 per hour. The machine does not have to be stopped once it is running. Machine B takes 30 minutes to set up and can then widgets at the rate of 60 per hour, but every 2 hours the machine has to be stopped and lubricated. Lubrication takes 30...

The company has two machines that produce certain items. Machine 1 produces 40 % of the...

The company has two machines that produce certain items. Machine 1 produces 40 % of the the items, and machine 2 produces 60% of the items. Machine 1 produces 3% of defective items and machine 2 produces 5% of defective items. a. The probability that a randomly selected produced item is defective is _________ b. If a randomly selected item is found to be defective, probability that it is produced on machine 2 is___________

Tocserp is considering the purchase of a new machine that will produce widgets. The widget maker...

Tocserp is considering the purchase of a new machine that will produce widgets. The widget maker will require an initial investment of $12,000 and has an economic life of five years and will be fully depreciated by the straight line method. The machine will produce 1,400 widgets per year with each costing $2.00 to make. Each will be sold at $4.50. Assume Tocserp uses a discount rate of 14 percent and has a tax rate of 34 percent. What is...

A factory has three machines capable of producing widgets. All three machines together can produce 191...

A factory has three machines capable of producing widgets. All three machines together can produce 191 widgets per hour. Machine A and machine B together can produce 129 widgets per hour, while machine A and machine C can together produce 137 widgets per hour. How many widgets per hour can each machine produce? A factory has three machines capable of producing widgets. All three machines together can produce 242 widgets per hour. Machine A and machine B together can produce...

Starliper Industries has developed a project to produce a new product: Widgets. To develop the widgets,...

Starliper Industries has developed a project to produce a new product: Widgets. To develop the widgets, Starliper Industries needs to purchase a new machine that will help develop the widgets. Starliper Industries is deciding between two different machines, “New Tech” and “Standard Classic” that have the capabilities necessary to develop the widgets. Your job will be to compare the two different machines using net present value. The company has produced the following information regarding the widgets and the two machines:...

"A company is considering two types of machines for a manufacturing process. Machine A has an...

"A company is considering two types of machines for a manufacturing process. Machine A has an immediate cost of $75,000, and its salvage value at the end of 6 years of service life is $21,000. The operating costs of this machine are estimated to be $3600 per year. Extra income taxes are estimated at $2300 per year. Machine B has an immediate cost of $43,000, and its salvage value at the end of 6 years' service is negligible. The annual...

A company has to choose between two new machines, the Alpha and the Beta. Both machines...

A company has to choose between two new machines, the Alpha and the Beta. Both machines would cost $30 000 and have an expected lifetime of 4 years. Estimates of the annual cash inflows which each machine would generate are given below Machine Year 0 1 2 3 4 Alpha Cash flow -$30,000 $14,000 $15,000 $15,000 $14,000 Beta Cash flow -$30,000 $8,000 $13,000 $15,000 $21,500 The company staff decides that 12% is an appropriate discount rate. Find the net present...

1. Cooper Copper Company is considering the purchase of two new molding machines. Machine A and...

1. Cooper Copper Company is considering the purchase of two new molding machines. Machine A and Machine B both have a cost of $10,000 and will be evaluated using a 12% cost of capital. The machines’ expected net cash flows are as follows: Expected Net Cash Flows Year Machine A Machine B 0 -$10,000 -$10,000 1 6,500 3,500 2 3,000 3,500 3 3,000 3,500 4 1,000 3,500 a. Calculate each project’s payback period. b. Calculate each project’s discounted payback period....

Problem #3 Company needs to decide between two machines. Machine C costs 10,000 and produce after...

Problem #3 Company needs to decide between two machines. Machine C costs 10,000 and produce after tax cash flows of 4,000 per year for 3 years. No salvage. Machine D costs 14,000 and produce after tax cash flows of 3,000 per year for 7 years. No salvage. Discount rate is 8% Which machine would you recommend?

Q.3. Alia company is considering the purchase of a new machine. Two alternative machines C and...

Q.3. Alia company is considering the purchase of a new machine. Two alternative machines C and D have been suggested, each having an initial cost of 520,000 SR and requiring 30,000 SR as additional working capital at the end of first year. Earning after taxation are expected to be as follows: Years Cash Inflows Machine C (SR) Cash Inflows Machine D (SR) 1 136,000 160,000 2 148,000 180,000 3 175,000 215,000 4 190,000 185,000 The company has targeted...