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# A fruit Basket has 20 apples and 10 oranges out of which 5

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Director
Joined: 07 Jun 2004
Posts: 627
Location: PA
Followers: 2

Kudos [?]: 105 [0], given: 22

A fruit Basket has 20 apples and 10 oranges out of which 5 [#permalink]  07 May 2005, 10:48
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
Director
Joined: 31 Aug 2004
Posts: 611
Followers: 2

Kudos [?]: 11 [0], given: 0

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 !!
SVP
Joined: 25 Nov 2004
Posts: 1503
Followers: 5

Kudos [?]: 19 [0], given: 0

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.
VP
Joined: 30 Sep 2004
Posts: 1496
Location: Germany
Followers: 4

Kudos [?]: 26 [0], given: 0

20/30*19/29+22/30*21/29=842/870=421/435
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If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Director
Joined: 07 Jun 2004
Posts: 627
Location: PA
Followers: 2

Kudos [?]: 105 [0], given: 22

guys thts not the right answer
SVP
Joined: 25 Nov 2004
Posts: 1503
Followers: 5

Kudos [?]: 19 [0], given: 0

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
Director
Joined: 07 Jun 2004
Posts: 627
Location: PA
Followers: 2

Kudos [?]: 105 [0], given: 22

still not correct mate
VP
Joined: 30 Sep 2004
Posts: 1496
Location: Germany
Followers: 4

Kudos [?]: 26 [0], given: 0

rxs0005, whats OA ? i think i dont agree with it !
_________________

If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Director
Joined: 07 Jun 2004
Posts: 627
Location: PA
Followers: 2

Kudos [?]: 105 [0], given: 22

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
SVP
Joined: 03 Jan 2005
Posts: 2258
Followers: 12

Kudos [?]: 175 [0], given: 0

Good one rxs. Correct answer would be P(2apples)+P(2nondamaged)-P(2nondamagedapples).
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Director
Joined: 31 Aug 2004
Posts: 611
Followers: 2

Kudos [?]: 11 [0], given: 0

Good one Rsx. I was really surprised by my too high calculation and was expecting something like this P(A+B)...
VP
Joined: 18 Nov 2004
Posts: 1448
Followers: 2

Kudos [?]: 12 [0], given: 0

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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