Quick probability question If there is an $80\%$ chance of rain in the next hour, what is the percentage chance of rain in the next half hour?
Thanks.

You could assume that occurrence of rain is a point process with constant rate lambda.  Then the process is Poisson and the probability of  rain in an interval of time [0,t] is given by the exponential distribution and if T = time until the event rain then 
P[T<=t] = 1-exp(-λt) assuming λ is the rate per hour then P(rain in 1 hour)=1-exp(-λ).
and P(rain in 1/2 hour)=1-exp(-λ/2).  Other models for the point process would give different answers.
In general the longer the time interval greater the chance of rain.
