Probablity question

Rahul@gurome wrote:Probability that it rains on a particular day is 1/2.
So the probability that it does not rain on a particular day is 1 - 1/2 = 1/2.
Hence the probability that it rains exactly 3 days out of 5 is 5C3*(1/2)^3 * (1/2)^2 = 10/32 = 5/16.

Hence the probability that it rains exactly 3 days out of 5 is 5C3*(1/2)^3 * (1/2)^2 = 10/32 = 5/16.

5C3 --- 5C3 is to choose 3 days out of 5 days,

(1/2)^3 ------ (1/2)^3 It will rain on 3 days or it will not rain 3 days, { Not Sure }

(1/2)^2---- I Don't Know What it is for??????????????

Please Explain................

goyalsau wrote:
(1/2)^3 ------ (1/2)^3 It will rain on 3 days or it will not rain 3 days, { Not Sure }

Yes. The 3 days it will rain. So (1/2)*(1/2)*(1/2) = (1/2)^3

goyalsau wrote: (1/2)^2---- I Don't Know What it is for??????????????

Probability of remaining two days it will NOT rain.

One questions guys....if I change the question a bit, will it make any difference:
The probablity that it will rain on any given day is 1/2. What is the probablity that it will rain < I have removed exactly from here> 3 days out of 5 days of weekdays?

The Jock wrote:One questions guys....if I change the question a bit, will it make any difference:
The probablity that it will rain on any given day is 1/2. What is the probablity that it will rain < I have removed exactly from here> 3 days out of 5 days of weekdays?

shouldn't make a difference, as the exactly is sort of implied. The question usually includes exactly to prevent any possible ambiguity (a question has to "hold up in court"). the other common form of these questions is "at least" (e.g. what is the probability that it will rain on at least 3 days?), which requires a different approach; your question uses "exactly" to guard against this misinterpretation of the question.