Question

In a certain agricultural region the probability of a drought during the growing season is 0.29, the probability of a severe cold spell is 0.26, and the probability of both is 0.15. Find the probability of the following.

(a) either a drought or a severe cold spell


(b) neither a drought nor a severe cold spell


(c) not having a drought

Answer 1

Let A be the event 'a drought' and B be the event 'severe cold spell'.
(a)

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`
Plugging in the given values , we get:

`P(A\ or\ B)=0.29+0.26-0.15=0.4`

(b)
P(neither a drought nor a severe cold spell) = 1.0 - 0.4 = 0.6.

(c)
P(not having a drought) = 1.00 - 0.29 = 0.71.