The weatherman tells you that there is a 70% chance of rain each day for the next 3 days. What is the probability that it will rain 2 out of the 3 days?

Answer 1

The chances that it will rain exactly 2 out of 3 days is:

_NC_R(p)^R(q)^(N-R)

where

C = Combination symbol

N = total number of days

R = Number of rain days

p = probability that it will rain

q = probability that it will not rain

So,

₃C₂(7/10)²(3/10)^(3-2) = (3!/(2!(3-2)!))(7/10)²(3/10)¹ = .441

or

There is a 44.1% chance that it will rain 2 of the 3 days