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# M04-09

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Math Expert
Joined: 02 Sep 2009
Posts: 51101

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15 Sep 2014, 23:22
1
12
00:00

Difficulty:

65% (hard)

Question Stats:

50% (00:59) correct 50% (00:59) wrong based on 214 sessions

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The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability that exactly two visitors will buy a pack of candy?

A. 0.343
B. 0.147
C. 0.189
D. 0.063
E. 0.027

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Joined: 02 Sep 2009
Posts: 51101

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15 Sep 2014, 23:22
3
2
Official Solution:

The probability that a visitor at the mall buys a pack of candy is 30%. If three visitors come to the mall today, what is the probability that exactly two visitors will buy a pack of candy?

A. 0.343
B. 0.147
C. 0.189
D. 0.063
E. 0.027

The event when 2 out of 3 visitors Buy a pack of candy can occur in $$\frac{3!}{2!}=3$$ ways: BBN, BNB, NBB ($$\frac{3!}{2!}=3$$ is basically the # of permutations of 3 letters out of which 2 B's are identical).

Now, each B has the probability of 0.3 and N has the probability of $$1-0.3=07$$, so $$P(B=2)=\frac{3!}{2!}*0.3^2*0.7=0.189$$.

Or you can directly apply the formula: if the probability of a certain event is $$p$$ (0.3 in our case), then the probability of it occurring $$k$$ times (2 times in our case) in $$n$$-time (3 in our case) sequence is:
$$P = C^k_n*p^k*(1-p)^{n-k}$$
$$P = C^k_n*p^k*(1-p)^{n-k}= C^2_3*(0.3)^2*(1-0.3)^{3-2}=\frac{3!}{2!}*0.3^2*0.7=0.189.$$

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Joined: 24 Nov 2014
Posts: 18

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19 Mar 2015, 11:34
Why do we multiply times 3 and not times 6?

Indeed the arrangement 0,3 * 0,3 * 0,7 has 3 combinations if order doesnt matter, but as order matters it must be 3!/(3-2)! = 6. Because they are distinct visitors so 0,3(tom) * 0,3(matt) * 0,7(joe) != 0,3(matt) * 0,3(tom) * 0,7(joe)

Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 51101

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20 Mar 2015, 04:56
Why do we multiply times 3 and not times 6?

Indeed the arrangement 0,3 * 0,3 * 0,7 has 3 combinations if order doesnt matter, but as order matters it must be 3!/(3-2)! = 6. Because they are distinct visitors so 0,3(tom) * 0,3(matt) * 0,7(joe) != 0,3(matt) * 0,3(tom) * 0,7(joe)

Thanks!

When there are 3 visitors out of which 2 buy, there can be 3 cases only: BBN, BNB, NBB.
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Joined: 17 May 2015
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09 Jul 2015, 07:31
Need help, How to use a slot method for this question ,
Math Expert
Joined: 02 Sep 2009
Posts: 51101

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09 Jul 2015, 07:54
apple08 wrote:
Need help, How to use a slot method for this question ,

Check different approaches HERE and HERE.
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Joined: 17 May 2015
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10 Jul 2015, 23:43
Many thankss
This type of question always make me confuse, how to improve my understanding, do I need to remember the formula,hope to hear from you
Many thankss
Manager
Joined: 12 Feb 2015
Posts: 119
Location: India
Concentration: Technology, Operations
GMAT 1: 680 Q50 V31
GPA: 3.9
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10 Jul 2015, 23:49
5
Ans C
In the simplest way :
apple08 , Bunuel:
There are 3 people and we need to chose exactly 2 who buy it.
So,
0.3*0.3*0.7 (Bcz other person would not bu has to be taken into consideration here)
=0.063

We can do this is 3 ways, different selections.
therefore, 0.063*3 =0.189

Please hit KUDOS if it helped you!!
Intern
Joined: 17 May 2015
Posts: 32

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11 Jul 2015, 14:41
Many thanksss
Current Student
Joined: 28 Jun 2014
Posts: 34
Location: Singapore
Concentration: General Management, Real Estate
GMAT 1: 690 Q49 V34
GPA: 3.37
WE: General Management (Real Estate)

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09 Aug 2015, 06:46
1
I think this is a high-quality question. There is a typing error.

1-0.3=0.7

not 07
Math Expert
Joined: 02 Sep 2009
Posts: 51101

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17 Aug 2015, 02:28
rahulcurrent wrote:
I think this is a high-quality question. There is a typing error.

1-0.3=0.7

not 07

Thank you. Will edit.
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10 Dec 2015, 06:55
I would like to know why orders matter in this case.
Thank you
Retired Moderator
Joined: 23 Sep 2015
Posts: 381
Location: France
GMAT 1: 690 Q47 V38
GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)

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28 Apr 2016, 05:00
nattiya27 wrote:
I would like to know why orders matter in this case.
Thank you

I doesn't its a combination question: The way of choosing the 2 that will buy out of 3: 3C2 = 3
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Manager
Joined: 28 Dec 2016
Posts: 88
Location: United States (IL)
Concentration: Marketing, General Management
Schools: Johnson '20 (M)
GMAT 1: 700 Q47 V38

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26 Jan 2017, 20:25
I have a question.

I calculated my answer by simply (0.3)(0.3)(0.7) = 0.063

I thought this was the way we calculate probabilities...
Now, do we multiply by 3 because we are asked for the possibility that EXACTLY two people out of three buy candy?

If we were to be asked a question without the mentioning of EXACTLY, would it make any difference?

In what cases can we just multiply the possibility of outcomes and what cases do we have to multiply the result by the total possible outcomes, which in this case is 3?

Thank you!
Math Expert
Joined: 02 Sep 2009
Posts: 51101

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27 Jan 2017, 06:18
conneryeon001 wrote:
I have a question.

I calculated my answer by simply (0.3)(0.3)(0.7) = 0.063

I thought this was the way we calculate probabilities...
Now, do we multiply by 3 because we are asked for the possibility that EXACTLY two people out of three buy candy?

If we were to be asked a question without the mentioning of EXACTLY, would it make any difference?

In what cases can we just multiply the possibility of outcomes and what cases do we have to multiply the result by the total possible outcomes, which in this case is 3?

Thank you!

We are multiplying by 3 because the case when two out of three buys candy can occur in three different ways: BBN (first buys, second buys, third does not buy), BNB, NBB.

Check different approaches HERE and HERE.

Theory on Combinations

DS questions on Combinations
PS questions on Combinations

Tough and tricky questions on Combinations

Theory on probability problems

Data Sufficiency Questions on Probability
Problem Solving Questions on Probability

Tough Probability Questions

Hope it helps.
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Posts: 356
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Concentration: Strategy, Marketing
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30 Jul 2018, 07:24
Question does not say that order matters.
So I just used: .3* .3 * .7

what is here which indicates that the order matters??
Am I missing something?? I am confused about how to determine that Order is of importance here?
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Re: M04-09 &nbs [#permalink] 30 Jul 2018, 07:24
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# M04-09

Moderators: chetan2u, Bunuel

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