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M04-09

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M04-09  [#permalink]

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New post 15 Sep 2014, 23:22
1
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A
B
C
D
E

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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Re M04-09  [#permalink]

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New post 15 Sep 2014, 23:22
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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:
\(P = C^k_n*p^k*(1-p)^{n-k}\)
\(P = C^k_n*p^k*(1-p)^{n-k}= C^2_3*(0.3)^2*(1-0.3)^{3-2}=\frac{3!}{2!}*0.3^2*0.7=0.189.\)


Answer: C
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Re: M04-09  [#permalink]

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New post 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)

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New post 20 Mar 2015, 04:56
madmax1000 wrote:
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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Re: M04-09  [#permalink]

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New post 09 Jul 2015, 07:31
Need help, How to use a slot method for this question ,
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Re: M04-09  [#permalink]

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New post 09 Jul 2015, 07:54
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New post 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
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Re: M04-09  [#permalink]

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New post 10 Jul 2015, 23:49
5
Ans C
In the simplest way :
apple08 , Bunuel:
P(Buying candy)=0.3
So, P(Not buying)=0.7
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!!
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New post 11 Jul 2015, 14:41
Many thanksss
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Re M04-09  [#permalink]

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

1-0.3=0.7

not 07
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New post 17 Aug 2015, 02:28
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Re: M04-09  [#permalink]

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New post 10 Dec 2015, 06:55
I would like to know why orders matter in this case.
Thank you
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Re: M04-09  [#permalink]

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New post 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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Re: M04-09  [#permalink]

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

I calculated my answer by simply (0.3)(0.3)(0.7) = 0.063
and got the wrong answer.

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!
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Re: M04-09  [#permalink]

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New post 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
and got the wrong answer.

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.

Combinatorics Made Easy!

Theory on Combinations

DS questions on Combinations
PS questions on Combinations

Tough and tricky questions on Combinations

Probability Made Easy!

Theory on probability problems

Data Sufficiency Questions on Probability
Problem Solving Questions on Probability

Tough Probability Questions

Hope it helps.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M04-09  [#permalink]

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New post 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?
Please Help..
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Re: M04-09 &nbs [#permalink] 30 Jul 2018, 07:24
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