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Louis14
Joined: 01 Nov 2019
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26 Feb 2020, 15:32
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When we say two events are independent, does it automatically mean AND rule? As in, I'm wondering wouldn't it be true if we used the Generalized OR Rule: P(A or B) = P(A) + P(B) - P(A AND B) if we said two events, A and B, are independent but we have to find the probability of either event A happens or B happens?
The bottom line is this: is there a scenario in which we use "addition" when we know two events are independent, or are all independent events meant to be multiplied?
The bottom line is this: is there a scenario in which we use "addition" when we know two events are independent, or are all independent events meant to be multiplied?
27 Feb 2020, 21:03
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Probability is from 0 to 1.
When you have 2 independent events ...
Let’s say that the possibility that A will happen is 0.6
the possibility that B will happen is 0.7
when you add up... it’s way over 1 which is totally impossible
1,A&B both happen : 0.6*0.7
2,Just one will happen : 0.6*0.3+0.4*0.7
3,Neither: 0.4*0.3
4, At least one : 1- neither=1-0.4*0.3 or both+just one = 0.6*0.7+ 0.6*0.3+0.4*0.6
1=both + just one + neither
Posted from my mobile device
When you have 2 independent events ...
Let’s say that the possibility that A will happen is 0.6
the possibility that B will happen is 0.7
when you add up... it’s way over 1 which is totally impossible
1,A&B both happen : 0.6*0.7
2,Just one will happen : 0.6*0.3+0.4*0.7
3,Neither: 0.4*0.3
4, At least one : 1- neither=1-0.4*0.3 or both+just one = 0.6*0.7+ 0.6*0.3+0.4*0.6
1=both + just one + neither
Posted from my mobile device
03 Mar 2020, 15:43
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Louis14
When we say two events are independent, does it automatically mean AND rule? As in, I'm wondering wouldn't it be true if we used the Generalized OR Rule: P(A or B) = P(A) + P(B) - P(A AND B) if we said two events, A and B, are independent but we have to find the probability of either event A happens or B happens?
You're correct. Here's an example:
"The probability that it will rain on Tuesday is 10%, and the probability that it will rain on Wednesday is 20%. If the weather on Wednesday and the weather on Tuesday are independent, what is the probability that it will rain on Tuesday OR Wednesday?"
Even though the problem says "or," you don't just add the two probabilities together, because you're talking about two separate events. Addition (the 'OR rule' ) is for considering multiple different ways that the same event could turn out. For instance, if they asks for the probability that it will rain OR snow on Tuesday, you'd be thinking about the or rule. But with independent events like this, you've got to start multiplying.
With regards to the problem I just made up, you'd solve it like this:
- Three possibilities will work: rain on both days, rain on just Tuesday, and rain on just Wednesday
- One possibility won't work: rain on neither day
- So, find the probability that it rains on neither day, and subtract from 1 to find the odds of the other possibilities
probability of NO rain on Tuesday and NO rain on Wednesday = .9 * .8 = .72
1 - .72 = .28
The answer is 28%, which isn't equal to 10% + 20%!
