The local weatherman reports that today the probability of rain is 0.45, the probability of a tornado is 0.35, and the probability of both is 0.12. What is the probability that it will rain today, given there is not a tornado?

probability that it will rain today, given there is not a tornado = 0.51

Step-by-step explanation:

We have to events in this question. Let:

A = It will rain

B = Tornado

B' = No Tornado

So, here we will use the conditional probability formula, which is given as:

P (A|B') = P (A∩B') / P (B')

where,

P (A|B') = probability that it will rain today, given there is not a tornado = ?

P (A∩B') = probability that it will rain and there will be no tornado

P (A∩B') = P (A) - P (A∩B) = 0.45 - 0.12 = 0.33

P (B') = Probability that there will be no tornado = 1 - P (B) = 1 - 0.35 = 0.65

Therefore,

P (A|B') = 0.33/0.65

P (A|B') = 0.51