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Probability that at least one of the event occurs is ?

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novice07
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Re: Probability that at least one of the event occurs is ? [#permalink] New post   10 Apr 2018, 01:37
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https://gre.myprepclub.com/forum/qotd-19-f ... tml#p18435
A similar question with official explanation
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mohan514
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Re: Probability that at least one of the event occurs is ? [#permalink] New post   11 Apr 2018, 09:18
Highest is atleast one of them happening, hence 0.2 or 0.3

Other option is when both occur 0.2*0.3 = 0.06

Hence the range is 0.06 to 0.3.

Please correct if wrong
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cyanApples
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Re: Probability that at least one of the event occurs is ? [#permalink] New post   11 Apr 2018, 09:22
novice07 wrote:
https://gre.myprepclub.com/forum/qotd-19-for-a-certain-probability-experiment-the-probabil-2639.html#p18435
A similar question with official explanation


Thanks a lot. That solution is perfect.

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Re: Probability that at least one of the event occurs is ? [#permalink] New post   11 Apr 2018, 09:25
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Either of the event occur, 0.2 or 0.3,

Both events occur = 0.2*0.3
=0.06

So the range is 0.06 to 0.3

Please correct if my answer is wrong
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Re: Probability that at least one of the event occurs is ? [#permalink] New post   03 May 2018, 16:50
1
0.44
P( at least one event occur ) = 1-P(no event occurring )

P( no event occurring) = [1-P(A)] *[1-P(B)] =(1-0.2)*(1-0.3) =0.8*0.7=0.56

Hence P( at least one event occur ) = 1-0.56 =0.44

Please correct if I’m wrong
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halam
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Re: Probability that at least one of the event occurs is ? [#permalink] New post   10 May 2018, 12:47
novice07 wrote:
Peter wrote:
novice07 wrote:
If P(A) = 0.8 and P(B) = 0.7, then Events A and B have to be independent for P(A and B) to be 0. Since they are not (which we assume when not given otherwise) there must be some intersection of these events.
So, if P(A) is 0.8 and P(B) is 0.7 then P(A and B)maximum would be 1, since it can't exceed 1.



Your concept is weak. For independent events, events are said not to affect each other, but they can both occur.

For example, the tail of a coin can occur with a dice rolling 6.

however, mutually exclusively events would not allow both events to occur, for example the tail and the face of a coin can not both occur.

Also the it is the maximum of (A or B) NOT (A and B) is 1. you should draw 2 circles which one stands for P(A) 0.8, the other stands for P(B) 0.7. Then the maximum of (A and B) is 0.7 when P(B) 0.7 is included in P(A) 0.8.


That maximum of P(A or B) NOT (A and B) was an overlook. Sorry for that.

I know that independent events can occur together and in that case P(A and B) would be P(A)*P(B). Appreciate for the example. However, I just meant that P(A or B) can't be equal to 1.5 because if two events having probabilities 0.7 and 0.8, it is not possible to have zero intersection.



Hi guys!!
Do you know what is the correct answer for this question?
If we understand "Probability that at least one of the event occurs is" as "The probability that A or B or Both will occur?", the correct answer should be 0.3 to 0.5, right?
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Re: Probability that at least one of the event occurs is ? [#permalink] New post   11 May 2018, 04:20
cyanApples wrote:
So if P(A) = 0.8 and P(B) = 0.7 then max probability is 1.5 ? That doesnt seem right.

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Important thing to be noted. Probability of any event happening ranges between 0 and 1. Probability cannot have value beyond this range.
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Re: Probability that at least one of the event occurs is ? [#permalink] New post   28 Mar 2021, 22:28
cyanApples wrote:
Probability of an event A occurring is 0.2
Probability of an event B occurring is 0.3

What is the range of probabilities that at least one event will occur?


Assuming both A and B are independent events:

P(A) \(= 0.2\)
P(B) \(= 0.3\)

P(A occurs but B not) \(= (0.2)(0.7) = 0.14\)
P(B occurs but A not) \(= (0.8)(0.3) = 0.24\)
P(A and B both occur) \(= (0.2)(0.3) = 0.06\)
P(neither A nor B) \(= (0.8)(0.7) = 0.56\)

P(at-least one event occurs) \(= 1 - (0.8)(0.7) = 0.44\)

Range must be \(0.06\) to \( 0.44\)

Assuming both A and B are mutually exclusive events:

P(A) \(= 0.2\)
P(B) \(= 0.3\)

P(A and B) \(= 0.2 + 0.3 = 0.5\)

Range must be \(0.2\) to \( 0.5\)
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Re: Probability that at least one of the event occurs is ? [#permalink]
28 Mar 2021, 22:28
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