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by sana.noor » Tue Aug 06, 2013 1:05 am
There are y different travelers who each have a choice of vacationing at one of n different detinations. What is the probability that all y travelers will end up vacationing at the same destination?

A. 1/n!

B. n/n!

C. 1/n^y

D. 1/n^(y-1)

E. n/y^n

I dont have answer
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by macattack » Tue Aug 06, 2013 4:48 am
Probability= #desired outcome/ total outcome
Total outcome=n^y
All the people could go the same destination in n different way since there are n destinations

Answer= n/n^y--->1/n^(y-1)--->D

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by Brent@GMATPrepNow » Tue Aug 06, 2013 6:04 am
sana.noor wrote:There are y different travelers who each have a choice of vacationing at one of n different detinations. What is the probability that all y travelers will end up vacationing at the same destination?

A. 1/n!
B. n/n!
C. 1/n^y
D. 1/n^(y-1)
E. n/y^n
We can also solve the question using probability rules.

P(all go to same destination) = P(person A goes to any destination AND person B goes to same destination as person A AND person C goes to same destination as person A AND person D goes to same destination as person A . . . etc)
= P(person A goes to any destination) x P(person B goes to same destination as person A) x P(person C goes to same destination as person A) x person D goes to same destination as person A) . . . etc
= (1) x (1/n) x (1/n) x (1/n) . . . etc

NOTE: If there are n destinations, and person A has selected one of them, then the probability is 1/n that an individual will select the same one. ALSO, if there are y people altogether, then there are y-1 people OTHER THAN person A.

So, moving along . . .
= (1) x (1/n)^(y-1)
= (1/n)^(y-1)
= D

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by [email protected] » Tue Aug 06, 2013 11:16 am
Hi sana.noor,

In these sorts of questions, it often helps to TEST values; this will give you a real-world example that will help you to find the correct answer.

For this prompt, I'm going to TEST:
y = 3
n = 4

So if there are 3 travelers and 4 possible destinations...let's figure out the probability...

The first traveler picks a destination (it can be any destination, so the first person doesn't matter)
The second traveler has a 1/4 chance of picking the same destination as the first traveler
The third traveler has a 1/4 chance of picking the same destination as the other two travelers.

1(1/4)(1/4) = 1/16

Now, plug the values of y and n into the answers. Only answer D matches, so you have the correct answer.

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by Uva@90 » Fri Aug 09, 2013 7:01 pm
macattack wrote:Probability= #desired outcome/ total outcome
Total outcome=n^y
All the people could go the same destination in n different way since there are n destinations

Answer= n/n^y--->1/n^(y-1)--->D
Hi Macattack,
I have basic doubt how the total probability be N^Y ? I am getting N*Y. Can you explain with an example. Please!

Thanks in advance.

Regards,
Uva

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by Matt@VeritasPrep » Sat Aug 10, 2013 12:39 pm
One quibble here: the question isn't terribly clear about whether we want all the travelers to be in the same place, or whether we want all the travels to be in one predetermined place. It does seem likely to imply they're all in one place, whichever that place is, though, so I can live with it. Let me explain each situation, however.

For example, say y = 4, n = 3 and our destinations are Brazil, Madagascar, and Timbuktu. The odds of all four people arriving in Timbuktu are obviously lower than the odds of all four people simply traveling to one of any of the three countries.

If I want everyone to arrive in Timbuktu, the odds are (1/3) * (1/3) * (1/3) * (1/3), as we have four people, and each has a 1/3 chance of arriving in Timbuktu. The odds are thus (1/3)�, and generally speaking, (1/n)^y.

If I want everyone to arrive in any country, however, the odds are (1/3) * (1/3) * (1/3) * (1/3) * 3. The odds of the travelers arriving in any one country remain the same, but there are now three countries in which they could arrive, so I multiply the odds by 3. That gives me (1/3)³, or generally speaking, (1/n)^y * n, or (1/n)^(y-1).

One note about the dangers of posting exponents in text - as you've written the answers, Sana, it makes it look like both D and E are correct. I get that by E you mean (n/y)^n, which is not the correct answer, but E could also read as n/(y^n) ... which is the correct answer. For all positive n and y, n/(y^n) = (1/n)^(y-1). Here's an image demonstrating the algebra:

Image

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by macattack » Sun Aug 11, 2013 10:50 pm
Uva@90 wrote:
macattack wrote:Probability= #desired outcome/ total outcome
Total outcome=n^y
All the people could go the same destination in n different way since there are n destinations

Answer= n/n^y--->1/n^(y-1)--->D
Hi Macattack,
I have basic doubt how the total probability be N^Y ? I am getting N*Y. Can you explain with an example. Please!

Thanks in advance.

Regards,
Uva
Hi Uva,
Sorry for the late reply but I was on holiday.
Now let's take a basic probability example to clear things up. If we want to throw a coin 3 times the total number of possible outcomes is: (HHH), (HHT), (HTH), (HTT), (THH), (THT), (TTH), (TTT) = 8
if we do it your way n*y=2*3=6 gives us the wrong answer.
The correct answer is 2^3=8
Hope it helped.