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will023
02-23-2010, 02:09 PM
Hi,

I have been struggling with this question for the past few days now and still can't seem to figure it out. If anyone can help me and show me how it is solved that would be awesome!

Question:

Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A) The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.

A)What is the probability that you will receive a Merit scholarship?

B)What is the probability of receiving the Athletic scholarship given that you have been awarded a Merit scholarship?

Martingale
02-23-2010, 07:51 PM
Hi,

I have been struggling with this question for the past few days now and still can't seem to figure it out. If anyone can help me and show me how it is solved that would be awesome!

Question:

Assume you have applied for two scholarships, a Merit scholarship (M) and an Athletic scholarship (A) The probability that you receive an Athletic scholarship is 0.18. The probability of receiving both scholarships is 0.11. The probability of getting at least one of the scholarships is 0.3.

A)What is the probability that you will receive a Merit scholarship?

B)What is the probability of receiving the Athletic scholarship given that you have been awarded a Merit scholarship?

for (a) use

http://latex.codecogs.com/gif.latex?P(A\cup M)=P(A)+P(M)-P(A\cap M)

for (b) use

http://latex.codecogs.com/gif.latex?P(A|M)=\frac{P(A\cap M)}{P(M)}

Outlier
02-23-2010, 08:10 PM
Venn diagrams are supposed to be easier
http://oscarbonilla.com/2009/05/visu...bayes-theorem/

If I understand this link correctly,

a Merit scholarship (M) and an Athletic scholarship (A) The probability that you receive an Athletic scholarship is 0.18.
If the area of the circle containing scholarships and their lack is 100, A's circle area is 18.

The probability of receiving both scholarships is 0.11.
An area of 11 is eclipsed in A's total area of 18, leaving 7.

The probability of getting at least one of the scholarships is 0.3.
Which means the area of no scholarships is = 70.

A)What is the probability that you will receive a Merit scholarship?
M's area must be 30 - 7 = 23, so P = 0.23.

B)What is the probability of receiving the Athletic scholarship given that you have been awarded a Merit scholarship?
11/23.

will023
02-24-2010, 10:00 AM
So would the two scholarships, A and M, be independent variables then? I think they would because getting one scholarship does not alter your chances of getting the other one right?

Martingale
02-24-2010, 10:57 AM
for (a) use

http://latex.codecogs.com/gif.latex?P(A\cup M)=P(A)+P(M)-P(A\cap M)

for (b) use

http://latex.codecogs.com/gif.latex?P(A|M)=\frac{P(A\cap M)}{P(M)}


Venn diagrams are supposed to be easier
http://oscarbonilla.com/2009/05/visu...bayes-theorem/

...

A)What is the probability that you will receive a Merit scholarship?
M's area must be 30 - 7 = 23, so P = 0.23.

B)What is the probability of receiving the Athletic scholarship given that you have been awarded a Merit scholarship?
11/23.

I think it is just as easy to use the formulas

filling in the numbers into the first equation

http://latex.codecogs.com/gif.latex?.3=.18+P(M)-.11

then solve

http://latex.codecogs.com/gif.latex?P(M)=.3-.18+.11=.23=\frac{23}{100}

and then


http://latex.codecogs.com/gif.latex?P(A|M)=\frac{P(A\cap M)}{P(M)}=\frac{.11}{.23}=\frac{11}{23}

Martingale
02-24-2010, 10:59 AM
So would the two scholarships, A and M, be independent variables then? I think they would because getting one scholarship does not alter your chances of getting the other one right?



is P(A|M)=P(A)?

will023
02-24-2010, 11:46 AM
is P(A|M)=P(A)?

No? I don't think so.

Martingale
02-24-2010, 11:51 AM
No? I don't think so.

then A and M are not independent