If the probability of rain on any given day in city x is 50%, what is the probability if with rain on exactly 3 days in a five day period?
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a probability problem, who can help? Thanks!
Source: Beat The GMAT — Problem Solving |
You have to find 5 arrangements over 3 posibilities:
5!/2!*3! = 10
And now work with the probabilities:
10 * [(1/2)^3]*[(1/2)^2] =
10 * 1/8 * 1/4 =
10/32
5/16
5!/2!*3! = 10
And now work with the probabilities:
10 * [(1/2)^3]*[(1/2)^2] =
10 * 1/8 * 1/4 =
10/32
5/16
For this problem you need to use the binomial distribution formula or you can lay every possible outcome out:billzhao wrote:If the probability of rain on any given day in city x is 50%, what is the probability if with rain on exactly 3 days in a five day period?
R=Rain
N=No rain
so your possible outcomes are
RRRNN=.5^5
NRRRN=" "
NNRRR=" "
RNRNR=" "
RRNRN=" "
RRNNR=" "
... AND SO ON
The easy way out is the one mentioned above. Using combinations 5 choose 3. Total 10 possible arrangements. Pr(rain)^3 * Pr(no rain)^2
and as above you get the same 5/16.
