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I must be stupid. I was wondering how I got it wrong so I went back to my numbers and somehow I multiplied by 7 when I had 8:
4/10)(3/9)(2/8 but mutliplied by 7) = 4/105 ... WTF?
I have another opinion on the third question. Wonder, if it is right?
1) I got 1/30 too 2) got 1/6 as well
But, in my opinion, the third question should be solved this way: the question asks what is the probability of AT LEAST one girl will be selected.
we have three mutually exclusive possibilities to select (they are all satisfy the asked condition): GBB (girl,boy,boy) GGB (girl,girl,boy) GGG (girl,girl,girl)
the probability of GGG is already known - 1/30. the probability of GGB is: 4/10*3/9*6/8 - 1/10. the probability of GBB is: 4/10*6/9*5/8 - 1/6.
As these are mutually exclusive, we shall add them together: 1/30+1/10+1/6 = 3/10.
I have another opinion on the third question. Wonder, if it is right?
1) I got 1/30 too 2) got 1/6 as well
But, in my opinion, the third question should be solved this way: the question asks what is the probability of AT LEAST one girl will be selected.
we have three mutually exclusive possibilities to select (they are all satisfy the asked condition): GBB (girl,boy,boy) GGB (girl,girl,boy) GGG (girl,girl,girl)
the probability of GGG is already known - 1/30. the probability of GGB is: 4/10*3/9*6/8 - 1/10. the probability of GBB is: 4/10*6/9*5/8 - 1/6.
As these are mutually exclusive, we shall add them together: 1/30+1/10+1/6 = 3/10.
What do you think of this?
ANS....... u r right but only mistake u r doing is that u have to multiply two of possiblities by 3....reason:- possiblities of taking two girls is GGB,GBG,BGG ie 1/10*3=3/10..... possiblities of taking two girls is GBB,BGB,BBG ie 1/6*3=1/2.... As these are mutually exclusive, we shall add them together: 1/30+3/10+1/2 = 5/6. _________________
Out of a classroom of 6 boys and 4 girls the teacher picks a president for the student board, a vice president and a secretary.
What is the probability that only girls will be elected?
What is the probability that only boys will be elected?
What is the probability that at least one girl will be elected?
Soln: All are permutations since even though we select 3 people , they are pushed into different posts. i.e. We could have selected the same 3 people, and arrange them in 6 different ways (3!) coz the posts that they take are different. president ,vice president and secretary.
What is the probability that only girls will be elected? Ans = 4P3/10P3
What is the probability that only boys will be elected? Ans = 6P3/10P3
What is the probability that at least one girl will be elected? Ans = (4P1 * 6P2 + 4P2 * 6P1 + 4P3)/10P3
If the teacher selects for president, vice pres & secretary, there are 3 distinct positions unlike say getting selected for a generic team where it doesn't matter what kind of position.
So girl 1 can be selected for pres, girl 2 for vp & girl 3 for secretary is a different case than girl 3 for pres, girl 2 for vp & girl 1 for secretary.
Can someone explain why we dont consider them distinct possibilities in this case? thanks.
IMO.. it shouldn't matter whether it is calculated with combinations or permutations. Reason being, if you consider the order in choosing the girls (numerator), you do the same in the denominator too. Hence it balances it out...
the results are coming out to be the same....
Cheers! JT _________________
Cheers! JT........... If u like my post..... payback in Kudos!!
|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|
Out of a classroom of 6 boys and 4 girls the teacher picks a president for the student board, a vice president and a secretary.
What is the probability that only girls will be elected?
What is the probability that only boys will be elected?
What is the probability that at least one girl will be elected?
Total comb = 10c3
1. Only girls = 4c3/10c3 = 1/30 2. Only boys = 6c3/10c3 = 1/6 3. Atleast one gurl = 1 - no gurl = 1 - only boys = 1 - 1/6 = 5/6 _________________
Cheers! JT........... If u like my post..... payback in Kudos!!
|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|
Re: Out of a classroom of 6 boys and 4 girls the teacher picks a [#permalink]
13 Jul 2013, 15:12
2
This post received KUDOS
Out of a classroom of 6 boys and 4 girls the teacher picks a president for the student board, a vice president and a secretary.
What is the probability that only girls will be elected?
What is the probability that only boys will be elected?
--------------------------------------------------------------------------------------------------------------------------------------------------------------- (1) What is the probability that only girls will be elected?
Just for practice, since the most efficient way to solve this problem is the Probability approach.
Encourage cooperation! If this post was very useful, kudos are welcome "It is our attitude at the beginning of a difficult task which, more than anything else, will affect It's successful outcome" William James
Re: Out of a classroom of 6 boys and 4 girls the teacher picks a [#permalink]
13 Jul 2013, 23:14
Expert's post
4
This post was BOOKMARKED
Maxirosario2012 wrote:
Out of a classroom of 6 boys and 4 girls the teacher picks a president for the student board, a vice president and a secretary.
What is the probability that only girls will be elected?
What is the probability that only boys will be elected?
--------------------------------------------------------------------------------------------------------------------------------------------------------------- (1) What is the probability that only girls will be elected?
Just for practice, since the most efficient way to solve this problem is the Probability approach.
Re: Out of a classroom of 6 boys and 4 girls the teacher picks a [#permalink]
06 Aug 2013, 20:46
(1). All girls are selected.
Just for argument sake, it has not been mentioned that One GIRL/BOY cannot be absorbed in multiple roles.
So why the probability P(All Girls) is not calculated as:
(4*4*4)/(10*10*10) = (8/125)
Desired outcome= You can fill each position in 4 ways or select each position in 4 ways Total outcome = You can make 10 selections each time
Please advise !!
Rgds, TGC ! _________________
Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________
gmatclubot
Re: Out of a classroom of 6 boys and 4 girls the teacher picks a
[#permalink]
06 Aug 2013, 20:46
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