Expert: Paul Klarreich - 10/20/2010

Question
during winter it rains 18 out of 30 days.5 winter days are selected at random.find the probability that,
(a)the first 2 days chosen will be fine and the remainder wet
(b)more rainy days than fine days are chosen.

Answer
Questioner:   athena
Country:  Australia
Category:  Advanced Math
Private:  No
 
Subject:  probability
Question:  during winter it rains 18 out of 30 days.5 winter days are selected at random.find the probability that,
(a)the first 2 days chosen will be fine and the remainder wet
(b)more rainy days than fine days are chosen.
....................................................
We will let  

s = p(sun), which = 2/5 and
r = p(rains), which is 3/5, of course.

So the first one is clearly  s^2 r^3.

The second one is a case of binomial probability, where:

p(3 rain, 2 sun) = C(5,3) r^3 s^2

p(4 rain, 1 sun) = C(5,4) r^4 s^1

p(5 rain, 0 sun) = C(5,5) r^5 s^0