Hi! Did not understand this QQ-
Here, the question says A occurs, and we are clearly given that prob. of A occuring is 0.3- how is the deduction here that I should take P(A) as 1 as per this framing- was confused in this, can you please guide me?
What do you mean?
\mathcal{P}(A) = 0.3 and \mathcal{P} (\neg B) = 1 - 0.6 = 0.4
Sorry my bad, should’ve clarified that this is actually the wrong answer.
The right answer here is 0.40. Greg has explained in the video that since P(A) gievn to occur, we take that as 1, and then multiply it with P(B) not occuring.
And I wasn’t able to grasp how did he take P(A) as 1, when P(A) ocurring is already given in the question.
I think he’s just trying to informally show you the definition of independence:
\mathcal{P} (\neg B \mid A) = \mathcal{P} (\neg B) = 0.4
That is, if A and B are independent events, then the following pair of events are also independent:
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\neg A and B
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A and \neg B
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\neg A and \neg B
Got it, I understood this.
In the question, I was still confused about the value of P(A). The question says, “given that event A occurs…”, and I know that probability of A = 0.3, so why did we take 1 here, adn multiplied that with P(B not occuring)?
You don’t. As I mentioned above, it might be an attempt to show you that the occurrence of A doesn’t affect the probability of B^C, because they are independent events.
understood, thanks!