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Probablilty of snow on Saturday

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Probablilty of snow on Saturday

by gmattesttaker2 » Thu May 29, 2014 7:58 am
Hello,

Can you please tell me how to solve for Statement 2:

If the probability of snow is the same every day this week, what is the probability of snow on Saturday?

1.The probability of snow on Monday is 1/7.
2.The probability having of no snow on both Thursday and Friday is 36/49.

OA: D

1) Since prob. of snow is the same every day this week => P(snow on Sat.) = 1/7 - [spoiler]Suff./spoiler]

2) P(No snow on Thu. and No snow on Fri.) = 36/49
=> P( Snow on Thu. and Snow on Fri. ) = 13/49

However, I was not able to solve from here.

Thanks for your help.

Regards,
Sri
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by Brent@GMATPrepNow » Thu May 29, 2014 8:13 am
gmattesttaker2 wrote: If the probability of snow is the same every day this week, what is the probability of snow on Saturday?

1) The probability of snow on Monday is 1/7.
2) The probability having of no snow on both Thursday and Friday is 36/49.
Target question: What is the probability of snow on Saturday?

Given: The probability of snow is the same every day this week

Statement 1: The probability of snow on Monday is 1/7.
If the probability of snow is THE SAME every day this week, then the probability of snow on Saturday is also 1/7
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The probability having of no snow on both Thursday and Friday is 36/49.
Let p = probability of snow on Saturday.
Since the probability of snow is the same every day this week, we know that p = probability of snow on Thursday and p = probability of snow on Friday.
Also, (1-p) = probability of NO SNOW on Thursday and (1-p) = probability of NO SNOW on Friday.

Statement 2 says: P(no snow on Thursday AND no snow on Friday) = 36/49
Rewrite as: P(no snow on Thursday) x P(no snow on Friday) = 36/49
Rewrite as: (1-p) x (1-p) = 36/49
Simplify: (1-p)² = 36/49
Solve: (1-p) = 6/7
So, p = 1/7
In other words, the probability of snow on Saturday is 1/7
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

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Brent
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by GMATGuruNY » Thu May 29, 2014 8:31 am
gmattesttaker2 wrote:Hello,

Can you please tell me how to solve for Statement 2:

If the probability of snow is the same every day this week, what is the probability of snow on Saturday?

1.The probability of snow on Monday is 1/7.
2.The probability having of no snow on both Thursday and Friday is 36/49.
Statement 1:
Since the probability of snow is the same for every day of the week, P(snow on Saturday) = 1/7.

Statement 2:
Test whether the value given in statement 1 -- P(snow) = 1/7 -- is the ONLY value that will satisfy statement 2.
If P(snow) = 1/7, then P(no snow) = 6/7.
Implication:
P(no snow on Thursday AND no snow on Friday) = 6/7 * 6/7 = 36/49.
This works.
NO OTHER FRACTION multiplied by itself will yield the required probability of 36/49.
Thus, like statement 1, statement 2 indicates that P(snow) = 1/7.
SUFFICIENT.

The correct answer is D.
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by Brent@GMATPrepNow » Thu May 29, 2014 9:44 am
gmattesttaker2 wrote:Hello,

Can you please tell me how to solve for Statement 2:

If the probability of snow is the same every day this week, what is the probability of snow on Saturday?

1.The probability of snow on Monday is 1/7.
2.The probability having of no snow on both Thursday and Friday is 36/49.

OA: D

1) Since prob. of snow is the same every day this week => P(snow on Sat.) = 1/7 - [spoiler]Suff./spoiler]

2) P(No snow on Thu. and No snow on Fri.) = 36/49
=> P( Snow on Thu. and Snow on Fri. ) = 13/49

However, I was not able to solve from here.

Thanks for your help.

Regards,
Sri
Hi Sri,

I've highlighted (in green) a small problem with your solution.
P(No snow on Thu. and No snow on Fri) = 36/49, this means that the probability of no snow on BOTH days is 36/49
If we want to apply the complement here, we can say that the probability of NOT HAVING no snow on BOTH days is 13/49. NOTE: This includes the possibility that there's no snow on ONE of the days and snow on the other day.
This conclusion is different from the conclusion that you drew. You concluded that 13/49 is the probability of having snow on both days. This is not true.

Cheers,
Brent
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