Probability

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Hira Javaid

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In a group of students, the probability that they get greater than 90% on their statistics test is 0.42, the
probability that they slept at least 8 hours the night before the test is 0.516, the probability that they study with other classmates is 0.432, the probability that they get marks greater than 90% on their test and slept at least 8 hours the night before the test is 0.244, the probability that study with classmates and slept at
least 8 hours before the quiz is 0.166, they probability that they get marks greater than 90% on their test and study
with classmates is 0.194, and probability that they do all three is 0.104.
Let A = getting greater than 90% on their test Let B = sleeping at least 8 hours Let C = studying with others
Determine the probability that a randomly selected student:
(a) gets marks greater than 90% on their test, but did not sleep at least 8 hours the night before the test?
(b) does not get greater than 90% and does not sleep at least 8 hours, given that you know they study with other
classmates?
Need help in solving this please.
 
Hira Javaid said:
In a group of students, the probability that they get greater than 90% on their statistics test is 0.42, the
probability that they slept at least 8 hours the night before the test is 0.516, the probability that they study with other classmates is 0.432, the probability that they get marks greater than 90% on their test and slept at least 8 hours the night before the test is 0.244, the probability that study with classmates and slept at
least 8 hours before the quiz is 0.166, they probability that they get marks greater than 90% on their test and study
with classmates is 0.194, and probability that they do all three is 0.104.
Let A = getting greater than 90% on their test Let B = sleeping at least 8 hours Let C = studying with others
Determine the probability that a randomly selected student:
(a) gets marks greater than 90% on their test, but did not sleep at least 8 hours the night before the test?
(b) does not get greater than 90% and does not sleep at least 8 hours, given that you know they study with other
classmates?
Need help in solving this please.
Click to expand...
I would start by making a Venn diagram and filling in what I can. If you want to approach it that way, please show how far you get. If you prefer another way, tell us about it.

Keep in mind that in order to help, we need to see what help you need. You have read this, right?

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...
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Yes
Dr.Peterson said:
I would start by making a Venn diagram and filling in what I can. If you want to approach it that way, please show how far you get. If you prefer another way, tell us about it.

Keep in mind that in order to help, we need to see what help you need. You have read this, right?

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...
www.freemathhelp.com
Click to expand...
I have read this sir!
I want to do it in a some way like bayes theorem or any other similar formula that would be easy if you can guide me according to that
 
Hira Javaid said:
Yes

I have read this sir!
I want to do it in a some way like bayes theorem or any other similar formula that would be easy if you can guide me according to that
Click to expand...
I've suggested something to try; if you think Bayes is easier, show us what you've done that makes you think that. If you haven't actually done any work yet, then try what I've suggested.

(This doesn't look like Bayes to me. It looks very much like a Venn diagram with three sets. And you may not even have to fill out the whole thing to answer the particular questions they've asked.)
 
Hira Javaid said:
(a) gets marks greater than 90% on their test, but did not sleep at least 8 hours the night before the test?
Click to expand...
This is not [imath]P(A | B)[/imath], but [imath]P(A\cap\overline{B})[/imath]. There is nothing conditional in this part.

Also, when you say
1633726869212.png
you are assuming A and B are independent. On what grounds do you make that assumption? In fact, you are given all three of these quantities, and the statement is not true!

Hira Javaid said:
(b) does not get greater than 90% and does not sleep at least 8 hours, given that you know they study with other
classmates?
Click to expand...
This asks for [imath]P(\overline{A}\cap\overline{B} | C)[/imath]. That is not

1633727129655.png
as you say it is.

Are you talking now about a different problem??
 
N
Dr.Peterson said:
This is not [imath]P(A | B)[/imath], but [imath]P(A\cap\overline{B})[/imath]. There is nothing conditional in this part.

Also, when you say
View attachment 29173
you are assuming A and B are independent. On what grounds do you make that assumption? In fact, you are given all three of these quantities, and the statement is not true!


This asks for [imath]P(\overline{A}\cap\overline{B} | C)[/imath]. That is not

View attachment 29174
as you say it is.

Are you talking now about a different problem??
Click to expand...
No i am talking about the same question. That was what i understood i am sorry sir. Can you tell me how to find \overline{A}
 
Hira Javaid said:
No i am talking about the same question. That was what i understood i am sorry sir.
Click to expand...
So you're saying you misunderstood the meaning of the problem. That is one of the reasons we ask to see your work, so we can tell where you might be thinking incorrectly.

Hira Javaid said:
Can you tell me how to find \(\overline{A}\)
Click to expand...
You may well use a different notation; this is one way to say "the complement of A". What notation do you use? It is also written as [imath]A^c[/imath] or [imath]A'[/imath]. And [imath]P(A')=1-P(A)[/imath].
 
Dr.Peterson said:
So you're saying you misunderstood the meaning of the problem. That is one of the reasons we ask to see your work, so we can tell where you might be thinking incorrectly.


You may well use a different notation; this is one way to say "the complement of A". What notation do you use? It is also written as [imath]A^c[/imath] or [imath]A'[/imath]. And [imath]P(A')=1-P(A)[/imath].
Click to expand...
Yes i know this notation. Thanks. I will do it and show you.
 
Dr.Peterson said:
So you're saying you misunderstood the meaning of the problem. That is one of the reasons we ask to see your work, so we can tell where you might be thinking incorrectly.


You may well use a different notation; this is one way to say "the complement of A". What notation do you use? It is also written as [imath]A^c[/imath] or [imath]A'[/imath]. And [imath]P(A')=1-P(A)[/imath].
Click to expand...
There is one more question sir..I am doing it but i am not 100% sure about its correctness. Can you help me with that also
 
This is where I tend to use a Venn diagram in order to see the relationship among the various sets.

Without that, you might just think about the relationship between [imath]P(A)[/imath], [imath]P(A\cap B)[/imath], and [imath]P(A\cap\overline{B})[/imath].
 
What to do next for part b?.. should i use the formula for P(A/B)=P(A and B)/P(B)... If yes how can i find P(A' ∩B' and C)
IMG_20211009_035456_325.jpg
 
The above step is wrong i think so..to find A'∩B' i have to find (A ∪ B)' then P(A'∩B')= 1- P(A ∪ B)'
is it correct?
 
Hira Javaid said:
What to do next for part b?.. should i use the formula for P(A/B)=P(A and B)/P(B)... If yes how can i find P(A' ∩B' and C)
Click to expand...
1633738705655.png

This is wrong. How much have you learned about set operations? Have you learned De Morgan's Laws?

But I still recommend making a Venn diagram, which helps tremendously in keeping track of relationships between the three sets. Have you tried doing what I suggest yet?
Hira Javaid said:
The above step is wrong i think so..to find A'∩B' i have to find (A ∪ B)' then P(A'∩B')= 1- P(A ∪ B)'
is it correct?
Click to expand...
Yes, that's right.
 
Dr.Peterson said:
View attachment 29178

This is wrong. How much have you learned about set operations? Have you learned De Morgan's Laws?

But I still recommend making a Venn diagram, which helps tremendously in keeping track of relationships between the three sets. Have you tried doing what I suggest yet?

Yes, that's right.
Click to expand...
Yes i have read De morgan's law..
I am finding it more difficult to do it by venn diagram Sir
 
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