Bunuel wrote:
If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a five-day period?
A. 3/32
B. 1/4
C. 9/32
D. 5/16
E. 1/2
Important not to miss ' in a row'..
At least three days means three cases...
1) 3 days in a row..
So take these three days as ONE R and other two as N
So NNR..
You can place R in 3C1=3 ways
2) 4 days.....4 days in a row OR 3 days in a row and 4th day of rain separated by a non rainy day
So take these three days as ONE R and non-rainy day as N and 4th day as r
So rNR........ rNR, rRN, RNr,rRN
4 ways
3) 5 days in a row
All 5 are one so one way
Total- 3+4+1=8
All possibilities=2*2*2*2*2=32
Probability=8/32=1/4
gmatnovice1122, what is wrong with your way..
Firstly you are complicating a simple way..
We use complement when we want to ease our calculations as normal scenario will have more casesIf talking of complement..
At least three days in a row means MAX two days in a row..
1) two days..
When there are 4 days of rains....RRNRR
When there are three days....RNNRR, NRNRR, ....many ways
When there are 2 days....RRNNN, NRRNN..and so on
2) one day..
4days is not possible
3 days..RNRNR
2 days ...NNRNR, and so on
3) none of the day
NNNNN... One way
So as you see it is more complicated, stick to normal