Probability

[akirac]

The hypermarket manager order 100 cartons of fruits from supplier A and 50 cartons of fruits
from supplier B. 5% of the cartons of fruits supply by supplier A are spoiled and 93% of the
cartons of fruits supply by supplier B are good. Answer the following questions.

Calculate the possible number of ways of arranging the 5 cartons from the supplier A and 5
cartons from supplier B in a line. Assume that the cartons from the same supplier are alike.

I'm not sure how to solve this, is it permutation or combination?

 

[Dr.Peterson]

The hypermarket manager order 100 cartons of fruits from supplier A and 50 cartons of fruits
from supplier B. 5% of the cartons of fruits supply by supplier A are spoiled and 93% of the
cartons of fruits supply by supplier B are good. Answer the following questions.

Calculate the possible number of ways of arranging the 5 cartons from the supplier A and 5
cartons from supplier B in a line. Assume that the cartons from the same supplier are alike.

I'm not sure how to solve this, is it permutation or combination?

It's neither (directly), though it is close.

The question is identical to asking how many "words" can be made by rearranging the letters AAAAABBBBB. Have you seen questions like that?

If not, you can use combinations. Imagine 10 blanks, _ _ _ _ _ _ _ _ _ _; you have to pick 5 places to put an A. How many ways can you do that?

 

[Deleted member 4993]

The hypermarket manager order 100 cartons of fruits from supplier A and 50 cartons of fruits
from supplier B. 5% of the cartons of fruits supply by supplier A are spoiled and 93% of the
cartons of fruits supply by supplier B are good. Answer the following questions.

Calculate the possible number of ways of arranging the 5 cartons from the supplier A and 5
cartons from supplier B in a line. Assume that the cartons from the same supplier are alike.

I'm not sure how to solve this, is it permutation or combination?

Please review your "translated" problem and check for accuracy. As written, the % of spoiled fruit does not have any significance..

In its simplest form, you have 10 spots and you want to place 5 cartons (assume from A) to place in there.

How many ways can you accomplish that?

 

[gq123]

em.....
how to solve this two question?
the title is same
1.Draw a well-label tree diagram to illustrate the above situation.
2.Calculate the total number of cartons of fruits which are spoiled.

 

[Dr.Peterson]

em.....
how to solve this two question?
the title is same
1.Draw a well-label tree diagram to illustrate the above situation.
2.Calculate the total number of cartons of fruits which are spoiled.

So these are subsequent parts of the same problem?

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[HuskyBoizz]

For this question,
Calculate the possible number of ways of arranging the 5 cartons from the supplier A and 5
cartons from supplier B in a line. Assume that the cartons from the same supplier are alike.
I do it like this.

10! / (5! * 5!)

is it correct ?

 

[Dr.Peterson]

For this question,
Calculate the possible number of ways of arranging the 5 cartons from the supplier A and 5
cartons from supplier B in a line. Assume that the cartons from the same supplier are alike.
I do it like this.

10! / (5! * 5!)

is it correct ?

Yes, that's the method I described in #2, using combinations. Since the OP has shown no further interest, I suppose there's nothing wrong in showing the answer now.

We still don't know how this question relates to all the information given in the first paragraph.

 

[gq123]

So these are subsequent parts of the same problem?

Please read this, and then comply with our rules by showing what you have tried:

READ BEFORE POSTING

Welcome to FreeMathHelp.com! Please take the time to read the following before you make your first post. It will help you to get your math questions answered promptly and in the most helpful manner. A summary is available here, but please read the complete guidelines below at your earliest...

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I'm not sure how to draw tree diagram...

 

[Dr.Peterson]

I'm not sure how to draw tree diagram...

Can you show the entire problem as given to you? There are two "situations" that have been mentioned, the one with 150 cartons, and the one with 5 from each supplier.

Try drawing a diagram, even if you are sure it is wrong, so we can see how close you are. Attach an image of it.

 

[HuskyBoizz]

The hypermarket manager order 100 cartons of fruits from supplier A and 50 cartons of fruits
from supplier B. 5% of the cartons of fruits supply by supplier A are spoiled and 93% of the
cartons of fruits supply by supplier B are good. Answer the following questions.
1. Calculate the possible number of ways of arranging the 5 cartons from the supplier A and 5
cartons from supplier B in a line. Assume that the cartons from the same supplier are alike.
(2 marks)
2. Draw a well-label tree diagram to illustrate the above situation. (8 marks)
3. Calculate the total number of cartons of fruits which are spoiled. (6 marks)
4. Are the events “number of cartons with spoiled fruits” and the “supplier” are independent?
Justify. (5 marks)
5. Given that a random selected carton of fruits is spoiled, calculate the probability that the
carton is supplier by supplier A.

This is the all the questions for this part.

I will show my answer for those questions and i want to know the more proper solution to get answers.

For question 1 ,
Calculate the possible number of ways of arranging the 5 cartons from the supplier A and 5
cartons from supplier B in a line. Assume that the cartons from the same supplier are alike.
10! / (5! * 5!) = 252 ways

For question 2,
Draw a well-label tree diagram to illustrate the above situation.


For question 3,
Calculate the total number of cartons of fruits which are spoiled.



For question 4,
Are the events “number of cartons with spoiled fruits” and the “supplier” are independent?
Justify.


For question 5,
Given that a random selected carton of fruits is spoiled, calculate the probability that the
carton is supplier by supplier A.

 

[Dr.Peterson]

It's interesting that you rounded your answer for #3. That tells us that the problem itself is wrong, considering that a carton is considered to be either spoiled or not (not half spoiled). Although we are not explicitly told what the "situation" is, it appears to be "selecting a carton randomly and determining whether it is spoiled."

An alternative way to get that answer is to look directly at the data in the problem:

• The hypermarket manager order 100 cartons of fruits from supplier A and 50 cartons of fruits from supplier B.
• 5% of the cartons of fruits supply by supplier A are spoiled ---> .05*100 = 5 cartons spoiled
• 93% of the cartons of fruits supply by supplier B are good ---> 0.07*50 = 3.5 cartons spoiled

So the total is 8.5 cartons. The problem doesn't tell us how to handle a half-spoiled carton! But I don't think rounding is appropriate.

We can also answer #4 more directly. The respective probabilities of spoilage are 5% and 7%; these are different, so spoilage is not independent of supplier. (Independence would require that the conditional probabilities are the same.)

For #5, I'm sure what you did is what is expected; but we could also observe directly that there are 8.5 spoiled cartons, 5 of which are from A. So P(A | S) = 5/8.5 = 10/17.