An n-sided die has sides labeled with the numbers 1 through n, inclusi

Question

An n-sided die has sides labeled with the numbers 1 through n, inclusive, and has an equal probability of landing on any side when rolled. If the die is rolled twice, what is the probability of rolling 1 both times?

(1) If the die is rolled twice, the probability that the two rolls are different is 80%.

(1) If the die is rolled twice, the probability that the two rolls are equal is 7/8.

Jenp · Accepted Answer

A is the correct answer.

From statement 1)

This statement is telling us the dice has exactly 5 faces, since there is no other possibility that two rolls show two different faces with probability 80%!

The probability that the two rolls are different is --> (5/5) * (4/5) = 4/5 = 0,8.

Now, the probability that the two rolls are NOT different is 1-0,8 = 1/5 = 0,2.

PAY ATTENTION: this is not the probability to get 1 twice, but the probability that ANY of number of the dice is rolled twice.

Since the probability to get one number is distributed EQUALLY on the n=5 faces, the probability to roll any of the 5 numbers twice is (1/5)/(5) = 0,04 = 4% which is exactly what we are looking for!

OR

Since we know by the initial observation that the dice has n=5 faces, we can calculate the probability that one of the five faces (#1) will be rolled twice:
(1/5) * (1/5) = 1/25 = 4/100 = 4% which is exactly what we are looking for!!

SUFFICIENT

From statement 2)

Let's reason ad absurdum:
if the dice only had 1 face we would always get number 1, so the probability to get 1 twice is 100%. 
If it had 2 faces, that is 2 numbers (1 and 2), the probability to get 1 twice would become 1/2 * 1/2= 1/4. 
As we increase the number of faces, we notice that the probability to get the same number twice only decreases (3 faces --> 1/9, 4 faces --> 1/16).
Since we are told the probability to get the same number twice is 7/8, which is greater than 1/4, we can say this is nonsense and the information is clearly NOT sufficient.

Hope this helps you,
kudos are very welcome!

Jenp

Mona2019 · Answer

IMO, D is the answer

From statement 1,
The probability that the two rolls are same = 1/5 (20%)
So the probability that the two rolls are 1 , is (1/5)*(1/5)
As the probability of getting two rolls same is 
nC1/n*1/n
And two rolls having a specific number same is 1/n*1/n

From statement 2,
1/n is 7/8
So probability of both rolls to have 1 is square of 7/8

I am not sure if I am right here , because my calculations for both the statements are giving different values.

Posted from my mobile device

Hama95 · Answer

the probability that the two rolls get you a different number is (4/5*4/5)=0.64, thus the probability that it gets u the same number can be 
1-0.64=0.36.

is this right ?

Aniki7376 · Answer

Here is how the answer goes in my opinion.

So probability to get 1 both times = (1/n)*(1/n) = 1/(n^2) (given the die has n sides)

Statement 1:

probability that 2 rolls are same = total same rolls/total possible rolls = n/(n^2) = 1/n = 1 - probability that 2 rolls are different = 1-0.8 = 0.2

i.e. 1/n = 0.2
SUFFICIENT

Statement 2:

probability that 2 rolls are same = 1/n = 7/8

SUFFICIENT

shouldn't the answer be D then??

or am i missing something. Please help.

fireagablast · Answer

So statement two is insufficient because it's "bad" information?
What's the point of statement two if the statement is impossible?

Jenp · Answer

Its purpose is to trick you!

fireagablast · Answer

I've never seen a question in which the statement was just an outright impossibility.

Jenp · Answer

Me neither to be honest, but this is not an official GMAT question

Crytiocanalyst · Answer

(1) If the die is rolled twice, the probability that the two rolls are different is 80%.
 nc1* n-1c1 / n^2 =8/10 
n=5 
Clearly sufficient

(1) If the die is rolled twice, the probability that the two rolls are equal is 7/8.
nc1 * 1/n^2 =7/8 
=> n=8/7 side of a cube doesn't make any sense therefore insufficient

Therefore IMO A

An n-sided die has sides labeled with the numbers 1 through n, inclusi

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GMAT Data Sufficiency (DS) Questions

An n-sided die has sides labeled with the numbers 1 through n, inclusi

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