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

Question

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

Funsho84 · Answer

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

nitinkarnwal · Answer

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

GMATinsight · Answer

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

Bunuel · Answer

Tank you. Done. Arranged options in ascending order as real GMAT questions have.

nitinkarnwal · Answer

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.

Hero8888 · Answer

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.

dmorgan1 · Answer

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

nitinkarnwal · Answer

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.

shoumkrish · Answer

We need to choose 3 fruits out of 6 which are not rotten. Since the order does not matter,

6C3/10C3 = 1/6

antarcticsugar · Answer

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.

fireagablast · Answer

10 total
6 good
4 rotten

6/10*5/9*4/8 = 1/6

bumpbot · Answer

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

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