probability of rain

Select 3 rainy days from 5 days,this can be done in 5C3 =10 ways.
Now on a day either it will rain or not rain,total number of possibilities in 5 days(called Sample space in probability)=2*2*2*2*2=32
[spoiler]The reqd. probability=10/32=5/16
Option C[/spoiler]

abhi332 wrote:f the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?

(A) 1/32

(B) 2/25

(C) 5/16

(D) 8/25

(E) 3/4
[spoiler]
OA:C[/spoiler]

For any probability function the answer will always be

total number of successful possiblities / total number of possibilities

Here, since its a binary function (it either rains or it doesnt) each day and each day is independant, the total number of combinations is

2^5 = 32

Because there are 5 days.

Now you want to know how many ways can you choose 3 rainy days (exactly) out of 5 total days. This is a simple example of the choose function.

5C3 = 10

Probability is 10 / 32 = 5/16

Choose (c)

Alternatively since this is a "small" problem you could count out all the examples of exactly 3 rainy days among 5.

We can sum this up as follows:

Probability = nCk/2^n where "n" is the number of times the event is being exercised, and k represents desired outcomes. You will almost certainly get a 50/50 probability question on test day.

abhi332 wrote:f the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?

(A) 1/32

(B) 2/25

(C) 5/16

(D) 8/25

(E) 3/4

Just to elaborate on Testluv's comment:

any time you have a series of independent events with a 50/50 probability split, you have a pseudo-coin flip question.

Accordingly, you can use the coin flip formula, which Testluv provided:

Probability of getting k results out of n flips = nCk/2^2

in which nCk represents the combinations formula, n!/k!(n-k)!.

So, here we have n=5 (5 days) and k=3 (we want rain exactly 3 times):

5C3/2^5 = (5!/3!2!)/32 = (5*4/2)/32 = 10/32 = 5/16

For more info on coin flip and pseudo-coin flip questions, check out:
https://www.beatthegmat.com/coin-flip-q ... html#75414

Thanks to Stuart's tricks on that page (link provided above). I was able to easily solve that in less than a minute using Pascal's triangle. Thanks Stuart