Symbolic form

[James Smithson]

Hello everyone! I was just hoping that possible someone could help me out on my question for school.

I have a bsic understanding and have guessed at the answer but there is nowhere in my textbooks that talk about this symbolic form.

Professor Humpty is writing a book about masks for which she is currently studying the collections of a museum. She notes that the masks in the collection are either shaped after a human face or an animal’s. And they are primarily constructed of either wood or metal.

Let H denote the event that the mask is shaped after a human face. And let W represent the event that the mask is primarily constructed of wood.

In particular, she observes that:
• among the collection, 60% of the masks are shaped after a human face
• among those masks that are shaped after a human face, the proportion of masks that are made of wood is 0.75.

(a) Write the information given in the two bullet points above in symbolic form, using the notation of the two events mentioned.

erm ..... thats my question but I dont really know where to begin......

Ihad a guess that → P (W|H)= 0.75/0.6..................................Am i correct ?

Im pretty sure im not but feel like im almost there

Wait a second ...
P(W AND H) = P(W|H) * P(H)
This is right .... I hope i just dont know if I have done what the question wanted and put it in symbolic form
That would mean that
P(W AND H) = 0.45

 

[lex]

If the experiment is choosing a mask at random, then the bullet points say:
P(H)=0.6
P(W|H)=0.75

Your conclusion that [MATH]P(W \cap H)=0.6\times 0.75 = \frac{9}{20}[/MATH] is correct.

 

[James Smithson]

If the experiment is choosing a mask at random, then the bullet points say:
P(H)=0.6
P(W|H)=0.75

Your conclusion that [MATH]P(W \cap H)=0.6\times 0.75 = \frac{9}{20}[/MATH] is correct.

thank you!!!

Could I please be cheeky and just ask one more thing as my english lets me down sometimes here. Are the events inderpendant or depaendant I believe them to be dependant and my understanding is that is a got a wood mask of a human it would change the odds of the next mask.


Once again thank you for your answer it really helps

 

[lex]

We don't have enough information to say that. They may or may not be independent. We would need some extra info. e.g. what proportion of the collection are Wooden.

 

[James Smithson]

We don't have enough information to say that. They may or may not be independent. We would need some extra info. e.g. what proportion of the collection are Wooden.

We don't have enough information to say that. They may or may not be independent. We would need some extra info. e.g. what proportion of the collection are Wooden.

I have managed to work out that 80% are wooden 20% metal 60% human 40% animal

I think that the events corresponding to the construction material of a mask and its shape are independent

 

[lex]

I have managed to work out that 80% are wooden 20% metal 60% human 40% animal

I think that the events corresponding to the construction material of a mask and its shape are independent

You can't have worked that out from the information you posted. If you have more information can you post the whole question.
How are you testing for independence? (If 80% are wooden, then they are not independent events).

 

[James Smithson]

You can't have worked that out from the information you posted. If you have more information can you post the whole question.
How are you testing for independence? (If 80% are wooden, then they are not independent events).

Hi lex sorry for the late reply after completing the questions we got a full table of % later on and thats the one i spoke about.

my last question is

"Are the events corresponding to the construction material of a mask and its shape independent? Give a reason for your answer."

I did an chi squared test that proves they are independant but I know I must be missing an easier way to say why they are independant I can not simply put for the answer they are independant because the chisquared test prooves the hypothesis of independance cannot be rejected

 

[JeffM]

It would greatly help if you answered our questions fully. You got “a full table of percents.” What are they and what do they represent? You want us to think about a problem but are unwilling to disclose it.

 

[James Smithson]

My question is Are the events corresponding to the construction material of a mask and its shape independent?


here is my table :

	Wood	Metal	Total
Human	45	15	60
Animal	35	5	40
Total	80	20	100

I dont know where to begin please could someone please help ( i have to prove they are I know the formular to work out independednt events but It does not help me as i dont know what im supposed to do with it )

 

[Dr.Peterson]

What is the definition of independence that you were given?

What happens if you apply it to these numbers? (The first step will be to translate the numbers in the table to probabilities.)

We need to see that in order to help. (The definition can be stated in different ways.)

 

[James Smithson]

What is the definition of independence that you were given?

What happens if you apply it to these numbers? (The first step will be to translate the numbers in the table to probabilities.)

We need to see that in order to help. (The definition can be stated in different ways.)

Not really been given a definition the numbers in the table are percentages and with it all adding to 100% I presume the probability is as simple as just putting 0.45 or 0.05 instead of 45 and 5 respectively.

I am really stuck with what theybwant from me. I found a formula
P(A∩B) = P(A) * P(B)

But I have no idea how I apply that to the question I asked.

I did a chi squared test to try prove independence but I think that's wrong


I am willing to answer all therlse questions but I really don't know how. Maybe it's better I attach the worksheet??

 

[James Smithson]

Here is what I have and it's the last part I am stuck on.


Sorry for been a pain and I really want to say thank you to everyone that's tried to help

 

[Dr.Peterson]

Here is what I have and it's the last part I am stuck on.

Why didn't you follow the guidelines and provide the entire question in the first place? This is important.

In post #6 you made a statement that depends on the information in (c), which you never told us!

Not really been given a definition the numbers in the table are percentages and with it all adding to 100% I presume the probability is as simple as just putting 0.45 or 0.05 instead of 45 and 5 respectively.

I am really stuck with what they want from me. I found a formula
P(A∩B) = P(A) * P(B)

But I have no idea how I apply that to the question I asked.

I did a chi squared test to try prove independence but I think that's wrong

The definition is, indeed, that events A and B are independent if P(A∩B) = P(A) * P(B).

So, if A = wood and B = human, what are P(A), P(B), and P(A∩B)? Is the equation true?

That's all you need. The chi-square test is far more advanced than this.

 

[lex]

The first bullet point and your answer to (d) have different values. This is enough to show they are not independent. If the mask being human form and the mask manufactured from wood were independent events then P(H) would be equal to P(H|W).

 

[BABATY2K]

How do we calculate the part (e) of the question: probability of either shaped after human face or made of wood or BOTH? I guess this is

P(H or W) = P(H) + P(W) - P(H and W)

 

[pka]

How do we calculate the part (e) of the question: probability of either shaped after human face or made of wood or BOTH?I guess this is

P(H or W) = P(H) + P(W) - P(H and W)

Do you realize this question from June 2021?
Have you read replies #5 & #9. They can help you.
Try to answer and post your effort.