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Director
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A fruit Basket has 20 apples and 10 oranges out of which 5 [#permalink]
 07 May 2005, 11:48
A fruit Basket has 20 apples and 10 oranges out of which 5 apples and 3 oranges are damaged. If 2 fruits are picked form the basket what is the Proabability that either both are apples or both are not damaged
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Director
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Total number of ways 30C2
2 apples : 20C2
2 not damaged : 22C2
Prob = (20C2+22C2)/30C2 = (19.20/2+21.22/2)/(29.30/2)
=(190+231)/435= 421/435
Looks quite high !!
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SVP
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twixt wrote: Total number of ways 30C2
2 apples : 20C2
2 not damaged : 22C2
Prob = (20C2+22C2)/30C2 = (19.20/2+21.22/2)/(29.30/2)
=(190+231)/435= 421/435.Looks quite high !!
absoulutly agree with the process.
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SVP
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20/30*19/29+22/30*21/29=842/870=421/435
_________________
If your mind can conceive it and your heart can believe it, have faith that you can achieve it.
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Director
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guys thts not the right answer
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SVP
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rxs0005 wrote: guys thts not the right answer
let me take the different route:
total possibilities=30c2
apples = 20
damaged = 5
not-damages=15
oranges = 10
damaged = 3
not-damaged=7
prob = [both apples (20c2) +not damaged (7c2)]/30c2=221/435
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Director
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still not correct mate
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SVP
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rxs0005, whats OA ? i think i dont agree with it ! 
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Director
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ways u can pick the 2 fruits is 30C2
number of ways both are apples 20C2
number of ways (any fruit ) that are not damaged 22C2
But u could have both apple and are good apples that is there are 15 good apples so number of ways 15C2
so total probability is
20C2 /30C2 + 22C2 /30C2 - 15C2 /30C2 = 316/435
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SVP
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Good one rxs. Correct answer would be P(2apples)+P(2nondamaged)-P(2nondamagedapples). 
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keep on seeking, and you will find;
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Director
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Good one Rsx. I was really surprised by my too high calculation and was expecting something like this P(A+B)...
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SVP
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I think this is only correct, if "both" means that none of the fruits are damaged. I don't think "both are not damaged" means that. I think "both of the fruits are not damaged" shud mean that either none of them are damaged OR either one of them might be damaged but not all.
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