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# The probability that a visitor at the mall buys a pack of

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Math Expert
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Re: the prob that a visitor at the mall buys a pack of candy is [#permalink]

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24 Feb 2012, 13:20
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fortsill wrote:
where's the right answer posted? how do i know if i'm right?

I added the correct answer under the spoiler in the initial post. Below is a solution.

The probability that a visitor at the mall buys a pack of candy is 0.3. If 6 visitors came to the mall today, what is the probability that exactly 4 will buy candy?

Since the probability that a visitor buys a candy is 0.3, then the probability that a visitor DOES NOT buy a candy is 1-0.3=0.7.

We want the probability that exactly 4 visitors out of 6 will buy a candy, so the probability of BBBBNN (where B denotes a visitor who buys a candy and N denotes a visitor who does not buy a candy). Each B has the probability of 0.3 and each N has the probability of 0.7, so we have $$0.3^4*0.7^2$$.

Next, BBBBNN case can occur in # of different ways: NNBBBB, NBNBBB, NBBNBB, ... (first two visitors doesn't buy and next four does; first doesn't buy, second does, third doesn't and next three does; ...) Basically it's # of permutations of 6 letters BBBBNN out of which 4 B's and 2 N's are identical, so $$\frac{6!}{4!*2!}$$.

Finally $$P(B=4)=\frac{6!}{4!*2!}*0.3^4*0.7^2$$.

Check the following links for different scenarios similar problems:
probability-85523.html

Hope it helps.
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Re: The probability that a visitor at the mall buys a pack of [#permalink]

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05 Nov 2013, 10:49
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Re: The probability that a visitor at the mall buys a pack of [#permalink]

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03 Dec 2014, 16:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The probability that a visitor at the mall buys a pack of [#permalink]

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18 Feb 2016, 23:43
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The probability that a visitor at the mall buys a pack of [#permalink]

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12 Mar 2017, 05:06
bmwhype2 wrote:
The probability that a visitor at the mall buys a pack of candy is 0.3. If 6 visitors came to the mall today, what is the probability that exactly 4 will buy candy?

[Reveal] Spoiler:
$$\frac{6!}{4!*2!}*0.3^4*0.7^2$$

Why do we have to multiply $$\frac{6!}{4!*2!}$$ ?
I don't think the sequence in which people buy matters here. Does it ?

Bunuel, kindly help.
Math Expert
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Posts: 37573
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Kudos [?]: 99384 [0], given: 11022

Re: The probability that a visitor at the mall buys a pack of [#permalink]

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12 Mar 2017, 06:22
Shruti0805 wrote:
bmwhype2 wrote:
The probability that a visitor at the mall buys a pack of candy is 0.3. If 6 visitors came to the mall today, what is the probability that exactly 4 will buy candy?

[Reveal] Spoiler:
$$\frac{6!}{4!*2!}*0.3^4*0.7^2$$

Why do we have to multiply $$\frac{6!}{4!*2!}$$ ?
I don't think the sequence in which people buy matters here. Does it ?

Bunuel, kindly help.

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Re: The probability that a visitor at the mall buys a pack of   [#permalink] 12 Mar 2017, 06:22

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