Problem Solving

In Rwanda, the chance for rain on any given day is 50%. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?

a) 4/7
b) 3/7
c) 35/128
d) 4/28
e) 28/135

IMO C
(7C4)*(1/2^7)

The answer is correct. Could you provide explanation please?

Thanks

7C4 = number of combinations of days with rain and no rain say x=rainy day, y = non-rainy
so we can have a pattern xyxyxyx....
and probability for either case is 1/2 (50%) so for 7 days it will be 1/2*1/2...7 times = (1/2^7)

I came across other way to solve it using binomial probability distribution formula as well

P(f) = nCr * P(rainy day) * (1 - P(rainy day))^n-r
where n = 7 and r = 4 and P(rainy day) = 1/2

Got it ... Thanks!!

satish.nagdev wrote:7C4 = number of combinations of days with rain and no rain say x=rainy day, y = non-rainy
so we can have a pattern xyxyxyx....
and probability for either case is 1/2 (50%) so for 7 days it will be 1/2*1/2...7 times = (1/2^7)

I came across other way to solve it using binomial probability distribution formula as well

P(f) = nCr * P(rainy day) * (1 - P(rainy day))^n-r
where n = 7 and r = 4 and P(rainy day) = 1/2

I misread the question to mean that it rains on 4 consecutive days out of the 7 - for this would the answer be 4C3 * 0.5^7?

thks.

satish.nagdev

i agree with u

Whenever an event has a 50% chance of occuring,it can always be treated as a flipping of a coin question.
This question is the same as "what is the probability of getting 4H on 7 flips of a coin"

You can apply the formula :
P(k results on n flips) = nck/2^n

Here,K=4,N=7 and the answer on substitution is 35/128.