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

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!