How do i solve this possibility question

[Dell]

how do i solve this possibility question

a scientist does 2 experiments, whose outcomes are independent of each other.

the possibility of a positive result in experiment A is 0.9
the possibility of a positive result in experiment B is 0.7

what is the possibility of a positive outcome in at least one of the experiments?

what i think i am looking for is P(A∪B) since i want either P(A) or P(B) or P(A∩B)

the problem is that i don't have enough information,
the answer is 0.97, which is P(A)+P(B)-P(A)*P(B), but how do i get to this, am i wrong in saying that i am looking for P(A∪B) ? which equation can i use to find this answer?

 

[Office_Shredder]

What is the possibility neither experiment has a positive outcome?

How does this help you answer the question?

 

[Dell]

no not really, how can i find that possibility, i know that it is 1-P(A∪B), but how does that help

 

[Office_Shredder]

What is the probability of a negative result for each experiment? Then remember that the experiments are independent, so what is the probability that both A is negative and B is negative in terms of each individual probability

 

[Dell]

A negative - 0.1
B negative - 0.3

but from here what do i do, can i say that since they are independent P(A∪B)=P(A)+P(B), but that comes to more than 1,
i see what you are saying, for the negative reult 0.1*0.3, but what rule is this??

 

[HallsofIvy]

Assuming A and B are independent, $P(A\cap B)$= P(A and B)= P(A)P(B).

$P(A\cup B)$= P(A or B)= P(A)+ P(B)- $P(A \cap B)$
and that is P(A)+ P(B) only if $P(A \cap B)= 0$ (A and B are mutually exclusive) which can't be true if they are independent.