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# Probability problem watch

1. Hey guys,
Sorry for any changes in topic. I was taking this practice SATS test and encountered this probability question. Any ideas?
Q)In a report on high school graduation, it was stated that 85% of high school students graduate. Suppose three high school students are randomly selected from different schools. What is the probability that all graduate?

I would appreciate if you guys brief me about the steps involved as well.
2. 85/3?
If not its 2:56am im tired..
3. Im pretty sure a probability would involve a value between 0 and 1.85/3 dosent give you that.
Give this a hit tommorow...feelin more rejuvenated i guess.
5. So the probability of 3 people graduating is the same as 2 is the same as 1. So-85/100 or 0.85 right.
Thanks dude.

Q) Ryan is pursuing an Mba course. He has applied to 2 universities. The acceptance rate for applicants with similar qualifications is 25% for Uni A and 40% for Uni B. What is the probability that Ryan will be accepted at least by one of the two universities?

Appreciate the help
6. (Original post by sliksilver)
So the probability of 3 people graduating is the same as 2 is the same as 1. So-85/100 or 0.85 right.
Um, I'm not sure how you reached that conclusion, but no. What I'm getting at is that if person A graduates in some school, it doesn't affect the fact that person B graduates at another school (i.e. graduation is independent). How do you handle "and" probabilities when they're independent? Draw a tree diagram if you must.
7. I take it they're independant? In which case, it would be the product of each individual passing the test.

So, (85/100)^3 in this case.
8. The events are independent mean they do not affect each other. A guy from a university dosent affect someone from another university graduating. So would it be 0.85x0.85x0.85?
9. (Original post by sliksilver)
So the probability of 3 people graduating is the same as 2 is the same as 1. So-85/100 or 0.85 right.
Thanks dude.

Q) Ryan is pursuing an Mba course. He has applied to 2 universities. The acceptance rate for applicants with similar qualifications is 25% for Uni A and 40% for Uni B. What is the probability that Ryan will be accepted at least by one of the two universities?

Appreciate the help
bold: no.
Draw a tree diagram and follow the path that gives three students passing.

Again draw a tree diagram (PM me tomorrow if you want help with that), I havn't drawn one so the answer I'm about to give may be slightly incorrect, but I think the answer is:

0.4 + 0.25 +(0.4 x 0.25) = 0.75 = 75%

accepted by at least one means being accepted by one or being accepted by the other or being accepted by both.
10. Thanks guys but i still wouldnt have figured just by looking at the question that these events were independent and that you needed to times the probability to get to the answer.
11. (Original post by sliksilver)
Thanks guys but i still wouldnt have figured just by looking at the question that these events were independent and that you needed to times the probability to get to the answer.
Sometimes it is hard to tell if events are independant, but in your first question it says that 3 students were picked from different schools, this is informing you of independance, don't worry if you don't see it, I used to have major problems with it also, but practive makes perfect
12. accepted by at least one means being accepted by one or being accepted by the other or being accepted by both
thanks dude. The terminology always messes me up. I will PM you tommorow.
13. (Original post by sliksilver)
thanks dude. The terminology always messes me up. I will PM you tommorow.
Hi, I only saw that you quoted me because I looked on this page again, if you want to quote people use the quote button at the bottom of people's post, and write under the text that appears. When you do that people are sent a 'message' to say they have been quoted, so they know even if they don't return to the thread and have a look. I appologise if I sound patronising, however it is quite important

Yeah its OK, PM me tomorrow and I'll try to assist with your questions etc.

Take care.
14. (Original post by mathperson)
bold: no.
Draw a tree diagram and follow the path that gives three students passing.

Again draw a tree diagram (PM me tomorrow if you want help with that), I havn't drawn one so the answer I'm about to give may be slightly incorrect, but I think the answer is:

0.4 + 0.25 +(0.4 x 0.25) = 0.75 = 75%

accepted by at least one means being accepted by one or being accepted by the other or being accepted by both.
im not the best at maths so dont quote me on it, but i was taught if it says at least 1 (or summin like that) the best way to work it out, is to find the prob that they dont get in either then take that away from one.

in this case 0.75*0.6 = 0.45
1-0.45 = 0.55

god i hope i havnt made myself look like a tit :P
15. (Original post by mathperson)
bold: no.
Draw a tree diagram and follow the path that gives three students passing.

Again draw a tree diagram (PM me tomorrow if you want help with that), I havn't drawn one so the answer I'm about to give may be slightly incorrect, but I think the answer is:

0.4 + 0.25 +(0.4 x 0.25) = 0.75 = 75%

accepted by at least one means being accepted by one or being accepted by the other or being accepted by both.

The 0.4 * 0.25 represents accepted at both, which is correct.

The 0.4 therefore represents accepted at A AND rejected at B, so you want 0.4*0.75.

The 0.25 represents accepted at B AND rejected at A, so you want 0.25*0.6.

So the probability of being accepted in at least one is 0.4*0.75 + 0.25*0.6 + 0.4*0.25 = 0.55, which is also what the poster above has worked out in a more elegant way.
16. (Original post by Swayum)

The 0.4 * 0.25 represents accepted at both, which is correct.

The 0.4 therefore represents accepted at A AND rejected at B, so you want 0.4*0.75.

The 0.25 represents accepted at B AND rejected at A, so you want 0.25*0.6.

So the probability of being accepted in at least one is 0.4*0.75 + 0.25*0.6 + 0.4*0.25 = 0.55, which is also what the poster above has worked out in a more elegant way.

Thanks to the people that corrected me, as explained I havn't worked through it properly since it was very early in the morning when I posted, however at some point today I will, and I'll see how it goes.

Thanks
17. OK I've had a quick look:

P(accepted at uni' A) = 0.25
P(not accepted at uni' A) = 0.75
P(accepted at uni' B) = 0.40
P(not accepted at uni' B) = 0.60

P(accepted at at least 1 uni') = P(accepted by A and not B) + P(accepted by B and not A) + P(accepted by both A and B)

P(accepted by A and not B) = 0.25 x 0.60
P(accepted by B and not A) = 0.40 x 0.75
P(accepted by both A and B) = 0.40 x 0.25

adding these togeather does indeed give 0.55.

(OK its not 3am now lol , thanks guys!)
18. Hey guys,
Thanks for the help.

Q)A manager has just recieved the expense check for six of her employees. She randomly distributes the checks to six employees. What is the probability that exactly five of them will recieve the correct checks( checks with correct names)?

I am pretty sure it is 1/6, but I keep returning back to the bolded 'exactly' in the question wondering whether it could have any alternative meaning.

Any ideas?
19. (Original post by sliksilver)
Hey guys,
Thanks for the help.

Q)A manager has just recieved the expense check for six of her employees. She randomly distributes the checks to six employees. What is the probability that exactly five of them will recieve the correct checks( checks with correct names)?

I am pretty sure it is 1/6, but I keep returning back to the bolded 'exactly' in the question wondering whether it could have any alternative meaning.

Any ideas?

'At least x' means x or more.
Example; The probability that a randomly chosen person has swine flu is 0.05 (5%). in a group of 10 people, what is the probability that at least 5 have swine flu?
This question is asking what is the probability that 5 or more have swine flu? ie P(5 or 6 or 7 or 8 or 9 or 10 have swine flu)? don't worry about doing the question because I'm just using it to illustrate what is meant by 'at least'.

'Exactily x' means precisely x.
Example; Using the same uxample as above, find the probability that exactily 5 people have swine flu.
This question is simply asking P(5 people have swine flu).

I'll think properly about your question later, unless someone gets there before me. But concentrate for now on understanding the interpretations thing, and perhaps make some examples up yourself! any more questions about interpretations (including examples) then just ask .
20. (urgent)
Hey guys,

Q)Suppose P(A)=.45, P(B)=.20, P(C)=.35, P(E|A)=.10, P(E|B)=.05 and P(E|C)=0. What is P(E)?
Anyone have an idea how to go about it?
I realize P(EUC)=P(E)+P(C) as they are mutually exclusive.
I don't know where to go from there.

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Updated: January 31, 2010
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