Probablility PS

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theachiever: Master | Next Rank: 500 Posts; Posts: 116; Joined: Wed Oct 03, 2012 10:44 pmFollowed by: 1 member; Thanked: 5 times

by theachiever » Tue Jul 16, 2013 3:19 am

Gender Under 2.0 2.0-3.0 Over 3.0

Male 0.05 0.25 0.10

Female 0.10 0.30 0.20

"¢If the student selected is female, what is the probability that her GPA is between 2.0 and 3.0?
"¢If the GPA of the student selected is over 3.0, what is the probability that the student is male?
"¢What is the probability that the student selected is female or has a GPA under 2.0 or both?
"¢ Is GPA independent of gender?

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Source: Beat The GMAT — Problem Solving | Tue Jul 16, 2013 3:19 am

faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Tue Jul 16, 2013 4:28 am

I believe that the question is in a table format (3x3)

if the student selected is female, what is the probability that her GPA is between 2.0 and 3.0?
Answer - 0.3

If the GPA of the student selected is over 3.0, what is the probability that the student is male?
Answer - 0.1 / (0.1 + 0.2) = 1/3 = 0.33

What is the probability that the student selected is female or has a GPA under 2.0 or both?

Answer = 0.6 + 0.15 + 0.1 = 0.85

Is GPA independent of gender?
Yes ?

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jitsy: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Sun Dec 19, 2010 1:49 pmFollowed by: 2 members; Thanked: 11 times

by jitsy » Tue Jul 16, 2013 7:37 am

This involves conditional probability. The probability of A conditioned on B, denoted P(A|B), is equal to P(AB)/P(B). The division provides that the probabilities of all outcomes within B will sum to 1. Conditioning restricts the sample space to those outcomes which are in the set being conditioned on (in this case B).

Answering question 1

1) If the student selected is female, what is the probability that her GPA is between 2.0 and 3.0?

Here
P(A)= 0.3/0.6 = 0.5
P(B)= 0.6/1.0 = 0.6
P(A|B)= P(AB)/P(B)= P(A)*P(B)/P(B) = 0.5*0.6/0.6= 0.5

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theachiever: Master | Next Rank: 500 Posts; Posts: 116; Joined: Wed Oct 03, 2012 10:44 pmFollowed by: 1 member; Thanked: 5 times

by theachiever » Tue Jul 16, 2013 9:42 am

Thanks for the solutions guys.I appreciate the help

Experts can you please give your inputs about the problem if you can guide me about it,it would be helpful.

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Tue Jul 16, 2013 10:23 am

Let's do it!

The first question is asking what percentage of the females have a GPA of 3.0, so our probability is:

# of 3.0 females
----------------
Total # of females

= .3/.6 = .5 = 50%

The second question is similar

# of males over 3.0
-------------------
Total # of people over 3.0

= .1/.3 = 1/3 = 33.3..%

The third one is tricky: for the odds of AT LEAST ONE of two groups, we do (Odds A) + (Odds B) - (Odds of A + B).

So ...

Odds Female = .6/1 = 60%
Odds Under 2.0 = .15/1 = 15%
Odds Both = .1/1 = 10%

So 60% + 15% - 10% = 65%

The other way to find the odds of AT LEAST ONE of two things is to do 1 - (Odds of neither). So the odds that someone is NOT a female or a person with a GPA under 2.0 is .35 (Guys with 2.0-3.0 or Guys with 3.0+). So 1 - .35 = .65, or 65%.

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jitsy: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Sun Dec 19, 2010 1:49 pmFollowed by: 2 members; Thanked: 11 times

by jitsy » Thu Jul 18, 2013 9:38 am

Matt,

Could you please help me with the last part of the (Yes/No) question and also explaining the reasoning. Thank you. I think it is the same as the last part in the question below. Just need some guidance in answering questions like these.

On 43percent of days, the market actually goes up. On 12 percent of days, Peter predicts that the market will go up and it does. If we pick a day at random, what is the probability that:
"¢Peter will predict that the market will go up, or it will actually go up, or both?
"¢The market will actually go up given that Peter has predicted it will?
"¢Does the Stock market moves up independently of Peter's Prediction?

Matt@VeritasPrep wrote:Let's do it!

The first question is asking what peurcentage of the females have a GPA of 3.0, so our probability is:

# of 3.0 females
----------------
Total # of females

= .3/.6 = .5 = 50%

The second question is similar

# of males over 3.0
-------------------
Total # of people over 3.0

= .1/.3 = 1/3 = 33.3..%

The third one is tricky: for the odds of AT LEAST ONE of two groups, we do (Odds A) + (Odds B) - (Odds of A + B).

So ...

Odds Female = .6/1 = 60%
Odds Under 2.0 = .15/1 = 15%
Odds Both = .1/1 = 10%

So 60% + 15% - 10% = 65%

The other way to find the odds of AT LEAST ONE of two things is to do 1 - (Odds of neither). So the odds that someone is NOT a female or a person with a GPA under 2.0 is .35 (Guys with 2.0-3.0 or Guys with 3.0+). So 1 - .35 = .65, or 65%.

If you appreciated my post or even just my time trying to help, please don't forget to click on 'Thanks' and say "Piece o' Cake mate" at the same time.

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