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A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra

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nitinkarnwal
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A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   Updated on: 08 Apr 2018, 01:17
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A basket contains 10 fruits of which 4 are rotten. If 3 fruits are drawn from the basket, find the probability that none of the fruits drawn is rotten.

A. 1/6
B. 1/4
C. 2/5
D. 1/2
E. 2/3
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Originally posted by nitinkarnwal on 07 Apr 2018, 14:01.
Last edited by Bunuel on 08 Apr 2018, 01:17, edited 1 time in total.
Edited the question and added the options.
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Funsho84
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Re: A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   07 Apr 2018, 14:31
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4/10 = rotten so 2/5 = rotten.
6/10 = good so 3/5 = good.

Probability of good from 3 drawn = 3/5 * 2/4 * 1/3 = 6/60 = 1/10
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Re: A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   08 Apr 2018, 00:55
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What I think is:

According to the language of the question, 3 fruits are drawn simultaneously from the basket and are not drawn one by one.

Hence, P(none of the fruits drawn is rotten) = P (drawing a non-rotten fruit)= 6C3/10C3 = 1/6
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Re: A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   08 Apr 2018, 00:57
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nitinkarnwal wrote:
A basket contains 10 fruits of which 4 are rotten. If 3 fruits are drawn from the basket, find the probability that none of the fruits drawn is rotten.


Total Fruits = 10

Rotten = 4

NOT rotten = 10-4 = 6

Fruits to be picked = 3

Probability of none of the picked fruit rotten = 6C3 / 10C3 = 20 / 120 = 1/6

I hope this helps

Bunuel : You may please add the following options to the question to make it look like GMAT question

A) 1/2
B) 2/5
C) 1/4
D) 2/3
E) 1/6
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Re: A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   08 Apr 2018, 01:19
Expert Reply
GMATinsight wrote:
nitinkarnwal wrote:
A basket contains 10 fruits of which 4 are rotten. If 3 fruits are drawn from the basket, find the probability that none of the fruits drawn is rotten.


Total Fruits = 10

Rotten = 4

NOT rotten = 10-4 = 6

Fruits to be picked = 3

Probability of none of the picked fruit rotten = 6C3 / 10C3 = 20 / 120 = 1/6

I hope this helps

Bunuel : You may please add the following options to the question to make it look like GMAT question

A) 1/2
B) 2/5
C) 1/4
D) 2/3
E) 1/6


Tank you. Done. Arranged options in ascending order as real GMAT questions have.
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Re: A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   08 Apr 2018, 10:07
GMATinsight wrote:
nitinkarnwal wrote:
A basket contains 10 fruits of which 4 are rotten. If 3 fruits are drawn from the basket, find the probability that none of the fruits drawn is rotten.


Total Fruits = 10

Rotten = 4

NOT rotten = 10-4 = 6

Fruits to be picked = 3

Probability of none of the picked fruit rotten = 6C3 / 10C3 = 20 / 120 = 1/6

I hope this helps

Bunuel : You may please add the following options to the question to make it look like GMAT question

A) 1/2
B) 2/5
C) 1/4
D) 2/3
E) 1/6



GMATinsight
Bunuel

What is the problem in the below solution? Please help.

P(drawing 3 rotten fruits) + P (drawing 3 non-rotten fruits) = 1

So, P (drawing 3 non-rotten fruits) = 1 - P(drawing 3 rotten fruits)
= 1 - ( 4C3 / 10C3)
= 29/30

But the correct answer is 5/6.
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A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   Updated on: 08 Apr 2018, 12:15
nitinkarnwal wrote:
GMATinsight wrote:
nitinkarnwal wrote:
A basket contains 10 fruits of which 4 are rotten. If 3 fruits are
What is the problem in the below solution? Please help.

P(drawing 3 rotten fruits) + P (drawing 3 non-rotten fruits) = 1

So, P (drawing 3 non-rotten fruits) = 1 - P(drawing 3 rotten fruits)
= 1 - ( 4C3 / 10C3)
= 29/30

But the correct answer is 5/6.


What about P(R+2 non R) and let's say P(2 R and 1 non R)? So you take only 2 combination out of many possible. The sum of all will give you 1.

Originally posted by Hero8888 on 08 Apr 2018, 10:33.
Last edited by Hero8888 on 08 Apr 2018, 12:15, edited 2 times in total.
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Re: A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   08 Apr 2018, 11:06
nitinkarnwal wrote:
A basket contains 10 fruits of which 4 are rotten. If 3 fruits are drawn from the basket, find the probability that none of the fruits drawn is rotten.

A. 1/6
B. 1/4
C. 2/5
D. 1/2
E. 2/3


P(None are rotten) = (6/10)*(5/9)*(4/8)
P(None are rotten) = (3/5)*(5/9)*(1/2)
P(None are rotten) = (3/9)*(1/2)
P(None are rotten) = (1/3)*(1/2)
P(None are rotten) = 1/6
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Re: A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   08 Apr 2018, 12:10
Thanks for the clarification. but there are only 4 combinations possible in this case :

P (3 non-R) + P (2 non-R and 1 R) + P (1 non-R and 2 R) + P (3 R) =1 .

The other two combinations P (2 R and 1 non-R) and P(1 R and 2 non-R) are just the same as already counted.
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Re: A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   08 Apr 2018, 12:25
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We need to choose 3 fruits out of 6 which are not rotten. Since the order does not matter,

6C3/10C3 = 1/6
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Re: A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   15 Apr 2018, 11:12
I did mine like this:
6/10 x 5/9 x 4/8 = 1/6
6 because there are 6 of them which are not rotten.
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Re: A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   15 Apr 2020, 20:58
10 total
6 good
4 rotten

6/10*5/9*4/8 = 1/6
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Re: A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink] New post   06 Jan 2024, 02:38
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Re: A basket contains 10 fruits of which 4 are rotten. If 3 fruits are dra [#permalink]
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