If the probability of rain on any given day in Chicago during the summ

Hi All,

The most efficient way to answer this question is in understanding how the Combination Formula applies to the math involved. However, even if you don't fully understand that concept, you can still get to the correct answer with a bit of 'brute force.'

To start, you have to understand that since each day has two equally-likely outcomes ('rain' or 'not rain'), then the various arrangements of 5 days of weather = (2)(2)(2)(2)(2) = 32. Thus, the probability of having EXACTLY 3 rain days must be some fraction out of 32...

From this point, we just have to figure out how many options consist of just 3 rain days. We can 'map' those out rather easily...

RRRNN

RRNRN
RRNNR

RNRRN
RNRNR
RNNRR

NRRRN
NRRNR
NRNRR
NNRRR

10 total options out of 32. Reducing that fraction gives us... 10/32 = 5/16

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Hi VeritasPrepKarishma, Bunuel

For someone who is particularly weak at Probability and Combinatorics, where would you recommend practice for ground work?
I have read through the theory but the application for under 700 Questions is what I need to work on.

thanks in anticipation.

You can search for relevant tags (Probability, Below 600 and 600 - 700 level) on this forum itself.

Can someone explain why the formula is 5C3∗(1/2)^3∗(1/2)^2 instead of 5C3∗(1/2)^3∗(1/2)^5

I followed this example on another post on probability:
Example #1
Q.:If the probability of raining on any given day in Atlanta is 40 percent, what is the probability of raining on exactly 2 days in a 7-day period?
Solution: We are not interested in the exact sequence of event and thus apply formula #2:
P=C72∗0.42∗0.65

Note that the number of days in the two cases are different.
In our original question, we are talking about 5 days so probability of rain on 3 days will be (1/2)^3 and of no rain on 2 days will be (1/2)^2.

In the other question you mentioned, we are talking about 7 days so we have (1/2)^2 and (1/2)^5.

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