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Probability Challenge Question for the weekend

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Probability Challenge Question for the weekend

by Brian@VeritasPrep » Fri Sep 24, 2010 4:26 pm
One of our instructors just drew this question up and sent it to me...I thought it was a pretty good one:



The probability of rain on any particular day in November is 21% and the probability of snow on any November day is 10%. What is the probability that on a given day in November only one of the two events will occur?


(A) 25%
(B) 26.8%
(C) 28.9%
(D) 30.2%
(E) 31%

I'll be back on Monday to discuss!
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by diebeatsthegmat » Fri Sep 24, 2010 6:05 pm
Brian@VeritasPrep wrote:One of our instructors just drew this question up and sent it to me...I thought it was a pretty good one:



The probability of rain on any particular day in November is 21% and the probability of snow on any November day is 10%. What is the probability that on a given day in November only one of the two events will occur?


(A) 25%
(B) 26.8%
(C) 28.9%
(D) 30.2%
(E) 31%

I'll be back on Monday to discuss!
i am not sure if i will solve this one correctly cos i didnt sleep last night and totally tired now
but i will solve this by this way
rain: 21% not rain 79%
snowL10% and not snow 90%
there are 2 cases: it will rain in a given day and not snow or it will snow but not rain
21%*90%/100%+79*10/100=26,8
the answer is B right?
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by Brian@VeritasPrep » Mon Sep 27, 2010 10:20 am
Wow - really nicely done! The catch on this one, at least to me, is that you have to account for either rain or snow but not both.

You could also solve it by noting that:

The probability of "both" will be 21% * 10%, which equals 21/1000
The probability of "only rain" is "rain" minus "both", or 21/100 - 21/1000
The probability of "only snow" is "snow" minus "both", or 10/100 - 21/1000

So adding "only rain" + "only snow", you'd have 21/100 + 10/100 - 21/1000 - 21/1000

Simplify by combining like terms: 31/100 - 42/1000

Then find a common denominator of 1000 and finish: 310/1000 - 42/1000 = 268/1000 = 26.8%.

The above method always seems a bit tricky to people because you're subtracting "both" twice, but the logic demonstrates that you have to, because "both" is counted twice...in the probability of one thing and the probability of the other.
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by diebeatsthegmat » Mon Sep 27, 2010 5:39 pm
Brian@VeritasPrep wrote:Wow - really nicely done! The catch on this one, at least to me, is that you have to account for either rain or snow but not both.

You could also solve it by noting that:

The probability of "both" will be 21% * 10%, which equals 21/1000
The probability of "only rain" is "rain" minus "both", or 21/100 - 21/1000
The probability of "only snow" is "snow" minus "both", or 10/100 - 21/1000

So adding "only rain" + "only snow", you'd have 21/100 + 10/100 - 21/1000 - 21/1000

Simplify by combining like terms: 31/100 - 42/1000

Then find a common denominator of 1000 and finish: 310/1000 - 42/1000 = 268/1000 = 26.8%.

The above method always seems a bit tricky to people because you're subtracting "both" twice, but the logic demonstrates that you have to, because "both" is counted twice...in the probability of one thing and the probability of the other.
ohh i have been waiting for days to get the correct answer hihih, thanks a lot brian. it seems that people are busy preparing for the test days because the deadline for application to school is ending soon. :)
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by limestone » Mon Sep 27, 2010 7:01 pm
Thanks Brian for a really good question. My approach is:

In a given day, there is:
21% chance that it will rain
10% chance that it will snow
x% chance that it will BOTH rain and snow.

Thus:
percent chance that it will rain ONLY : 21% - x%
percent chance that it will snow ONLY: 10% -x%
percent chance that it will rain ONLY or snow ONLY: 21%+10% - 2*x% = 31% - 2*x%

To find x, find the product of chance of rain and chance of snow: 21% * 10* = 0.21*0.1 = 0.021 = 2.1%
The answer, therefore, is: 31% - 2*2.1% = 26.8%
"There is nothing either good or bad - but thinking makes it so" - Shakespeare.
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by Brian@VeritasPrep » Tue Sep 28, 2010 3:00 pm
Perfect, limestome - nicely done!

Diebeatsthegmat - glad you were waiting for the answer, and I hope the explanation was worth the wait! Yeah, this time of year is hectic in the GMAT/MBA admissions space...I love the energy and sense of urgency that it brings.

I'll throw up a few more questions this week, and on the main homepage here every day this week I'm posting a new challenge problem that deals with exponents and algebra, so look out for those, too!
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