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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # Probability that at least one of the event occurs is ?  Question banks Downloads My Bookmarks Reviews Important topics
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Intern Joined: 19 Mar 2018
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Kudos [?]: 9 , given: 4

Probability that at least one of the event occurs is ? [#permalink] 00:00

Question Stats: 62% (01:00) correct 37% (01:02) wrong based on 16 sessions
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?
Founder  Joined: 18 Apr 2015
Posts: 13883
GRE 1: Q160 V160 Followers: 313

Kudos [?]: 3672 , given: 12901

Re: Probability that at least one of the event occurs is ? [#permalink]
Expert's post
Please follow the rules for posting on the board. https://greprepclub.com/forum/rules-for ... -1083.html

Moreover, where are the answer choices ??

Thank you so much for your collaboration.

Regards
_________________ Intern Joined: 20 Mar 2018
Posts: 39
GRE 1: Q163 V149 GRE 2: Q168 V162 GPA: 3.5
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Kudos [?]: 40  , given: 8

Re: Probability that at least one of the event occurs is ? [#permalink]
1
KUDOS
Let's say the events are A and B. Essentially, we have to find the range of P(A or B)

P(A or B) = P(A) + P(B) - P(A and B)

The maximum probability of occurrence of any one of the events is when the events are mutually exclusive i.e. P (A and B) = 0. So, P(A or B) = 0.2 + 0.3 = 0.5
The minimum probability of occurrence of any one of the events is when the intersection is maximum i.e P(A and B) = 0.2. So, P(A or B) = 0.2 + 0.3 - 0.2 = 0.3

Range: 0.3 to 0.5
Intern Joined: 19 Mar 2018
Posts: 14
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Kudos [?]: 9 , given: 4

Re: Probability that at least one of the event occurs is ? [#permalink]
So if P(A) = 0.8 and P(B) = 0.7 then max probability is 1.5 ? That doesnt seem right.

Posted from my mobile device  Manager Joined: 27 Sep 2017
Posts: 111
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Kudos [?]: 47  , given: 4

Re: Probability that at least one of the event occurs is ? [#permalink]
1
KUDOS
cyanApples wrote:
So if P(A) = 0.8 and P(B) = 0.7 then max probability is 1.5 ? That doesnt seem right.

Posted from my mobile device OK, since you post the question, can you offer the Answer?
Intern Joined: 19 Mar 2018
Posts: 14
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Kudos [?]: 9 , given: 4

Re: Probability that at least one of the event occurs is ? [#permalink]
Well I'm unsure hence I posted ?

Posted from my mobile device  Manager Joined: 27 Sep 2017
Posts: 111
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Kudos [?]: 47  , given: 4

Re: Probability that at least one of the event occurs is ? [#permalink]
2
KUDOS
novice07 wrote:
Let's say the events are A and B. Essentially, we have to find the range of P(A or B)

P(A or B) = P(A) + P(B) - P(A and B)

The maximum probability of occurrence of any one of the events is when the events are mutually exclusive i.e. P (A and B) = 0. So, P(A or B) = 0.2 + 0.3 = 0.5
The minimum probability of occurrence of any one of the events is when the intersection is maximum i.e P(A and B) = 0.2. So, P(A or B) = 0.2 + 0.3 - 0.2 = 0.3

Range: 0.3 to 0.5

Though I agree with the maximum, but I have with minimum value. i think we can choose 0.2 NOT 0.3, since we think that at least B occur. then it would be 0.2.

range: 0.2-0.5.
Intern Joined: 20 Mar 2018
Posts: 39
GRE 1: Q163 V149 GRE 2: Q168 V162 GPA: 3.5
Followers: 1

Kudos [?]: 40 , given: 8

Re: Probability that at least one of the event occurs is ? [#permalink]
Peter wrote:
novice07 wrote:
Let's say the events are A and B. Essentially, we have to find the range of P(A or B)

P(A or B) = P(A) + P(B) - P(A and B)

The maximum probability of occurrence of any one of the events is when the events are mutually exclusive i.e. P (A and B) = 0. So, P(A or B) = 0.2 + 0.3 = 0.5
The minimum probability of occurrence of any one of the events is when the intersection is maximum i.e P(A and B) = 0.2. So, P(A or B) = 0.2 + 0.3 - 0.2 = 0.3

Range: 0.3 to 0.5

Though I agree with the maximum, but I have with minimum value. i think we can choose 0.2 NOT 0.3, since we think that at least B occur. then it would be 0.2.

range: 0.2-0.5.

You're correct.

Thanks Peter.
+1 Kudos Intern Joined: 21 Mar 2018
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Re: Probability that at least one of the event occurs is ? [#permalink]
4
KUDOS
0.44
Manager Joined: 27 Sep 2017
Posts: 111
Followers: 1

Kudos [?]: 47 , given: 4

Re: Probability that at least one of the event occurs is ? [#permalink]
oyetundekabiru wrote:
0.44

explain it, thanks

Last edited by Peter on 21 Mar 2018, 08:37, edited 1 time in total.
Manager Joined: 27 Sep 2017
Posts: 111
Followers: 1

Kudos [?]: 47 , given: 4

Re: Probability that at least one of the event occurs is ? [#permalink]
cyanApples wrote:
Well I'm unsure hence I posted ?

Posted from my mobile device Please give the source of the question.
Intern Joined: 19 Mar 2018
Posts: 14
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Kudos [?]: 9 , given: 4

Re: Probability that at least one of the event occurs is ? [#permalink]
It's from the actual GRE.

Posted from my mobile device Founder  Joined: 18 Apr 2015
Posts: 13883
GRE 1: Q160 V160 Followers: 313

Kudos [?]: 3672 , given: 12901

Re: Probability that at least one of the event occurs is ? [#permalink]
Expert's post
Sorry, could you tell us if this is a quantity comparison question or a multiple answer choice question ??

In the latter, could you provide the 5 answer choices ?'

Thank you for your collaboration. And please, when you post a question, post it in a proper manner and use the tags.

This way, you give a lot of help to the other students and the community as a whole.

Thank you, once again.

Regards
_________________
Intern Joined: 19 Mar 2018
Posts: 14
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Kudos [?]: 9 , given: 4

Re: Probability that at least one of the event occurs is ? [#permalink]
Hi, the question is a multiple choice question. And since It showed up on my GRE , I can't recollect the answer choices correctly. Although I do remember that the answer choices were ranges and one of the choice was 0.5 >= P >= 0.2.

Posted from my mobile device Intern Joined: 20 Mar 2018
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GRE 1: Q163 V149 GRE 2: Q168 V162 GPA: 3.5
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Kudos [?]: 40 , given: 8

Re: Probability that at least one of the event occurs is ? [#permalink]
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.

Last edited by novice07 on 21 Mar 2018, 23:28, edited 1 time in total.
Intern Joined: 19 Mar 2018
Posts: 14
Followers: 0

Kudos [?]: 9 , given: 4

Re: Probability that at least one of the event occurs is ? [#permalink]
novice07 wrote:
Events A and B have to be independent for P(A and B) to be 0.

Don't you mean dependent ?

Posted from my mobile device Intern Joined: 20 Mar 2018
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GRE 1: Q163 V149 GRE 2: Q168 V162 GPA: 3.5
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Kudos [?]: 40 , given: 8

Re: Probability that at least one of the event occurs is ? [#permalink]
No, I mean independent.
If P(A) = 0.7, P(B) = 0.8 and P(A and B)=0 then they must be independent events, which is not the case in this question. If they had given P(A) = 0.7 and P(B) = 0.8 in the question, they would have given certain value for P(A and B) as well.
Manager Joined: 27 Sep 2017
Posts: 111
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Kudos [?]: 47 , given: 4

Re: Probability that at least one of the event occurs is ? [#permalink]
novice07 wrote:
No, I mean independent.
If P(A) = 0.7, P(B) = 0.8 and P(A and B)=0 then they must be independent events, which is not the case in this question. If they had given P(A) = 0.7 and P(B) = 0.8 in the question, they would have given certain value for P(A and B) as well.

If P(A) = 0.7, P(B) = 0.8 and P(A and B)=0 then they must be independent events?

no, they are mutually exclusively events, which intersection would not be allowed.
Manager Joined: 27 Sep 2017
Posts: 111
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Kudos [?]: 47 , given: 4

Re: Probability that at least one of the event occurs is ? [#permalink]
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. Intern Joined: 20 Mar 2018
Posts: 39
GRE 1: Q163 V149 GRE 2: Q168 V162 GPA: 3.5
Followers: 1

Kudos [?]: 40  , given: 8

Re: Probability that at least one of the event occurs is ? [#permalink]
1
KUDOS
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. Re: Probability that at least one of the event occurs is ?   [#permalink] 23 Mar 2018, 03:47
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