Probability

Question

If the chance of an overnight freeze in Rexburg on any given night is 0.65, what is the probability that it will freeze one or more of the next 14 nights in Rexburg?

Answer 1

For this problem it is easiest to figure out the probability of the opposite of what is asked and then subtract that from 1.

(For exampe, if the chance that what I don't want is 0.25, then the chance of what I do want is 1 - 0.25 = 0.75)

 

In this case the opposite of "it will freeze one or more nights in 14" is:

"it will not freeze for each/all of the 14 nights".

 

The chance of not freezing is (1 - 0.65) = 0.35 each night,

so the chance of not freezing for 14 nights is:

  (0.35)¹⁴ ~ 4.14 x10^-7   very small!

and so the chance that it will freeze one or more nights is:

   1 - 4.14  x10^-7  = 0.999999586  or  99.9999586 %

Very likely!