A cupboard holds 10 cans, of which 3 contain pumpkin puree. If a group

Question

A cupboard holds 10 cans, of which 3 contain pumpkin puree. If a group of 4 cans is randomly selected from the cupboard, what is the probability that the group includes the 3 cans containing pumpkin puree?

A. 1/120
B. 1/30
C. 1/21
D. 3/10
E. 4/10

A. 1/120
B. 1/30
C. 1/21
D. 3/10
E. 4/10

stne · Answer

Total ways to select  4  cans from  10   cans  = 10_C_4 = 210  ways

Favourable ways =Choose all the  3  cans this can be done in  1  way only
 
and choose  1  from the remaining  7   in  7_C_1 = 7  ways

Probability=  \frac{1*7}{210} = \frac{1}{30}

Ans B

Hope it's clear.

PranjalGMAT · Answer

Is the below thought process correct?

If we select the 3 pumpin puree cans in the first 3 chances - the probability for the same is

3/10 * 2/9 * 1/8 * 7/7 = 1/120

But the above can be selected in 4 different ways (as the non-pumpkin puree jar can be seleted as first, second or third as well), so

1/120 * 4 = 1/30

Thus, Option B

Anchrs · Answer

Bunuel 
Probability for selecting 3 pumpkin puree cans and 1 empty can 
3/10 * 2/9 *1/8 * 7/7 = 120 ways so shouldn't it be 1/120. 
Why is multiplication by 4 required?
Also, how to decide when to multiply; why is the order of selection important here?

Krunaal · Answer

The order of selection is not important here, but when you solve it this way  "3/10 * 2/9 *1/8 * 7/7"  you're by default considering an arrangement where you first select 3 pumpkin and then 1 non-pumpkin, and hence it isn't a correct approach.

The right approach is to select 3 pumpkin cans => which can be done in only one possible way, and then select 1 of the 7 non-pumpkin cans => 7 ways.

Total no. of ways to select 4 of 10 cans => 10C4 = 210

Probability = 7/210 = 1/30

DonBosco7 · Answer

Multiplication by 4 is required because of the arrangement issue.

Basically we are choosing it this way for 4 positions-  puree   puree   puree   other

the above choice of "puree" and "other" can be picked in 4!/3! ways, here we divide by 3! because of repetition.

4!/3! = 4

DonBosco7 · Answer

cc:  Bunuel   hr1212 
Can someone please explain this question with a reverse probability !

Q - A cupboard holds 10 cans, of which 3 contain pumpkin puree. If a group of 4 cans is randomly selected from the cupboard, what is the probability that the group includes the 3 cans containing pumpkin puree?

reverse should be -

1 = p(includes puree) + p (do not include puree)

there are 10 cans 3 of which contain puree, this means 7 does not contain puree.

so if i try reverse

P(includes puree) = 1 - P(no puree)
 = 1 - 4/7*3/6*2/5*1/4
this yields an answer = 34/35

OR

P(includes puree) = 1 - 7C4/10C4

this yields an answer = 5/6

??? What am i missing here ???

hr1212 · Answer

You are missing the cases where you partially include puree cans. What about when you pick just 2 puree cans and 2 other ones?

When you consider all those cases, probability would add up to 1.

It's good that you are thinking multiple approaches to solve a question, but for this one the reverse probability approach would take ages to negate all cases. So the optimal approach would be the direct one.

A cupboard holds 10 cans, of which 3 contain pumpkin puree. If a group

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A cupboard holds 10 cans, of which 3 contain pumpkin puree. If a group

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