# What is the probability of a defective component from two companies?

• LDC1972
In summary, Lloyd provided a tree diagram that illustrates the probability of a component being defective from both companies. He calculated that the probability of a component being defective from company A is 60% or 0.6 and the probability of a component being defective from company B is 40% or 0.4. He also calculated that the probability of a component being defective is 0.012 if it is from company A and 0.016 if it is from company B. Finally, he provided a table that lists the probability of a component being defective for each company.
LDC1972

## Homework Statement

Components purchased from 2 companies.
Company A is 60% of total purchase with 2% defective parts.
Company B is 40% of total purchase with 1% defective parts.

Components from both companies are thoroughly mixed on receipt.

A/ Draw a tree diagram to represent possible outcomes when a single component is selected at random.

i/ What is the probability that this component cam from company A and is defective?
ii/ Calculate the probability the component was defective
iii/ If was defective, what is probability it was supplied by company A?

P(A U B)

## The Attempt at a Solution

Ok, this seems simple, I'd like to know if I'm doing the right thing here if possible please?

I didn't start with the tree (having never done / used this method before).

So I calculated probabilities.

i/ What is the probability that this component came from company A and is defective?

Probability supplied by A = 60% or 0.6
Probability defective if A = 2% or 0.02
Therefore;
0.6 x .02 = 0.012
So probability that this component came from company A = 0.6 (60%) and is defective = 0.012 (1.2%)

ii/ Calculate the probability the component was defective
I assume this incorporates both companies, so:
Company A = 0.6 (60%)
Company B = 0.4 (40%

As per question i/ 0.6 x 0.02 = 0.012 (1.2%)

Now for company B:
0.4 x 0.01 = 0.004 (0.4%)

Now add probability the component picked was defective = 0.012 + 0.004 = 0.016 (1.6%)

iii/ If was defective, what is probability it was supplied by company A?
Probability component from company A AND defective = 0.012 / 0.016 = 0.75 = 75% probability component was from company A and is then ALSO defective

For the tree I then drew vector lines at 45 degrees from start point, one line company A, othe company B. Company A I wrote 0.6 beside line, B I wrote 0.4 beside line. Continued B line to defective P(B U defective) = 0.4 x 0.01 = 0.004%

Continued a line to defective P(B U defective) = 0.6 x 0.02 = 0.012%

Tagged off both lines at 90 degrees mid point with company A P (U not defective) = .6 x .98 = 0.588

And line off Company B as P(U not defective) = 0.4 x 0.99 = 0.396

Many thanks

Lloyd

All your working before attempting to construct a tree looks right.
I was not able to follow your verbal description of the tree.

1 person
haruspex said:
All your working before attempting to construct a tree looks right.
I was not able to follow your verbal description of the tree.

Hi, thanks so much for your help.

I'll attach a real 'sketch' of what my tree is like:

Hopefully it is visible?

Thanks

Lloyd

#### Attachments

• tree.jpg
20.2 KB · Views: 1,565
LDC1972 said:
Hi, thanks so much for your help.

I'll attach a real 'sketch' of what my tree is like:

Hopefully it is visible?

Thanks

Lloyd

Probably helps to view at 200% and terrible writing reads:

Company A and company B
And defective / not defective

Thanks again

Lloyd

Yes, that looks ok, except you've written wrong numbers in the top and bottom lines. Factor of ten out. You previously posted
Continued B line to defective P(B U defective) = 0.4 x 0.01 = 0.004%
Continued a line to defective P(B U defective) = 0.6 x 0.02 = 0.012%
Each of which starts out correct, but you forgot to move the decimal point when adding the '%'.

1 person
Hi,

I re-did the whole thing yesterday (watched you tube maths help).

All figures came out as my originals plus I now have a tidy tree.

Used the long winded Bayes theorem too for iii/

Still got 0.75 so all cool.

I also dropped percentages altogether and kept everything as straight figures (no units) - as the textbook showed no units on their examples. Hope that was right thing to do? As you say, the figure must lay between 0 and 1.

Thanks.

Lloyd

Thank you for the help!

Last edited:

## What is a probability tree diagram?

A probability tree diagram is a visual representation of the possible outcomes of a probability experiment. It is a helpful tool in understanding and calculating the probabilities of different events.

## How do you create a probability tree diagram?

To create a probability tree diagram, start by drawing a vertical line to represent the main event. Then, for each possible outcome of the main event, draw a branch extending from the line. Continue to add branches for each subsequent event until all possible outcomes have been accounted for.

## How is a probability tree diagram useful?

A probability tree diagram is useful because it provides a clear and organized representation of all possible outcomes and their associated probabilities. This can be especially helpful in complex probability problems where there are multiple events and outcomes.

## What is the difference between a probability tree diagram and a Venn diagram?

A probability tree diagram shows the possible outcomes of a probability experiment, while a Venn diagram shows the relationships between different sets of data. Additionally, a probability tree diagram is typically used for calculating probabilities, while a Venn diagram is used for visualizing data.

## Are there any limitations to using a probability tree diagram?

While probability tree diagrams are a useful tool, they can become complex and difficult to read if there are too many events and outcomes. They also assume that the events are independent, meaning that the outcome of one event does not affect the outcome of another. Therefore, they may not be suitable for all types of probability problems.

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