A manufacturer of automotive g

A manufacturer of automotive gaskets has two plants, A and B.Plant A manufactures 65 % of the gaskets and plant B manufactures35 %. Because of a batch of faulty material from a companysupplying both plants, 3% of the gaskets are of sub-standardquality from plant A and 5% are sub-standard from plant B. Despiteyour internal quality control procedures, you still had asub-standard gasket returned from one of your customers. What isthe probability it came from plant B? i) Illustrate your answerwith an event tree and ii) show how to calculate the value usingBayes Equation. b) Using Bayes Theorem, solve the following twoproblems: 1. A couple has three children, the eldest of which is aboy. What is the probability that they have three boys? 2. A couplehas three children, one of which is a boy. What is the probabilitythat they have three boys?

i)

ii)

Given,

P(A) = 0.65 and P(B) = 0.35

P(S | A) = 0.03 and P(S | B) = 0.05

Probability that sub standard quality came from plant B = P(B |S)

By law of total probability,

P(S) = P(S | A) P(A) + P(S | B) P(B)

= 0.03 * 0.65 + 0.05 * 0.35 = 0.037

By Bayes theorem,

P(B | S) = P(S | B) P(B) / P(S)

= 0.05 * 0.35 / 0.037

= 0.472973

1.

Probability that eldest is boy, P(E) = 1/2

Probability that they have three boys, P(3B) = (1/2)3= 1/8

Given that all three children are boys, Probability that eldestis boy , P(E | 3B) = 1

Given, the eldest of which is a boy. Probability that they havethree boys = P(3B | E)

= (E | 3B) P(3B) / P(E) {By Bayes theorem}

= 1 * (1/8) / (1/2)

= 1/4

2.

Probability that one of three children is boy, P(B) = 1 -Probability that all three are girls = 1 – (1/2)3 =7/8

Probability that they have three boys, P(3B) = (1/2)3= 1/8

Given that all three children are boys, Probability that one isboy , P(B | 3B) = 1

Given, the one of children is a boy. Probability that they havethree boys = P(3B | B)

= (B | 3B) P(3B) / P(B) {By Bayes theorem}

= 1 * (1/8) / (7/8)

= 1/7

"Our Prices Start at \$11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"
Calculate the price
Pages (550 words)
\$0.00
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with brilliantassignmenthelp.com
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
Testimonials
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
11,595
Customer reviews in total
96%
Current satisfaction rate
3 pages
Average paper length
37%
Customers referred by a friend
OUR GIFT TO YOU
15% OFF your first order
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat

Sometimes it is hard to do all the work on your own

Let us help you get a good grade on your paper. Get professional help and free up your time for more important courses. Let us handle your;

• Dissertations and Thesis
• Essays
• All Assignments

• Research papers
• Terms Papers
• Online Classes