kellogs4toniee wrote:If the probability of rain on any given day in City X is 50 percent, what is the probability that it rains on exactly 3 days in a 5-day period?
() 8/25
() 2/25
() 5/16
() 8/25
() 3/4
Please explain in detail how would you do this, and what concepts I should re-familiarize myself with for similar problems in the future.
Thank you!
Tony
First the answer: 5C3(1/2)^3(1/2) = 5/16
The concept here is that we could have YYYNN, YYNYN, NNYYY and we have to basically count all such events and divide by all possible events such as YYYYY, NYYYY etc. Where N - no rain, Y = rain. As you can see this can get really messy, hence some creative math minds of yore developed the
Binomial method, you might want to lok it up in detail but here is what I understand of it:
If the probability of an event occuring is "p" and this is independent across tries, then if an activity is carried out "n" times, the probability of
exactly "r" successes is given by:
nCr(p)^r(1-p)^r.
Some clarifications - "independent across tries" what is the probability of getting an Ace of spades from a deck = 1/52, if this is repeated again with replacement of the card picked what is the probability = 1/52 BUT if card is not replaced what is the probability = 1/51 (assuming the ace has not been already picked). Thus in the former case (when card replaced) the probability is independent, whereas in the latter they are not.
Some places where this can be applied - coin flips, rainy days, days when a temp will cross a certain number, dice roll, card picking.
Hope this is useful
