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Probability that at least one of the event occurs is ?

cyanApples

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

19 Mar 2018, 09:01

Quantity A	Quantity B
Probability of an event A occurring is 0.2	Probability of an event B occurring is 0.3

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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

D

Carcass

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

19 Mar 2018, 10:29

Expert Reply

1

Bookmarks

Please follow the rules for posting on the board. https://gre.myprepclub.com/forum/rules-for ... -1083.html

Moreover, where are the answer choices ??

Thank you so much for your collaboration.

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novice07

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

20 Mar 2018, 22:53

1

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

cyanApples

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

21 Mar 2018, 00:03

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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Peter

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

21 Mar 2018, 00:27

1

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?

cyanApples

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

21 Mar 2018, 00:30

Well I'm unsure hence I posted ?

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Peter

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

21 Mar 2018, 00:31

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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.

novice07

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

21 Mar 2018, 01:25

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.
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oyetundekabiru

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

21 Mar 2018, 06:26

4

0.44

Peter

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

Updated on: 21 Mar 2018, 08:37

oyetundekabiru wrote:

0.44

explain it, thanks

Originally posted by Peter on 21 Mar 2018, 08:22.
Last edited by Peter on 21 Mar 2018, 08:37, edited 1 time in total.

Peter

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

21 Mar 2018, 08:25

cyanApples wrote:

Well I'm unsure hence I posted ?

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Please give the source of the question.

cyanApples

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

21 Mar 2018, 09:31

It's from the actual GRE.

Posted from my mobile device

D

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

21 Mar 2018, 15:10

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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

cyanApples

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

21 Mar 2018, 18:14

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.

Sorry for incomplete answers.

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novice07

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

Updated on: 21 Mar 2018, 23:28

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.

Originally posted by novice07 on 21 Mar 2018, 21:18.
Last edited by novice07 on 21 Mar 2018, 23:28, edited 1 time in total.

cyanApples

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

21 Mar 2018, 22:23

novice07 wrote:

Events A and B have to be independent for P(A and B) to be 0.

Don't you mean dependent ?

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novice07

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

21 Mar 2018, 23:33

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.

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

22 Mar 2018, 22:45

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.

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

22 Mar 2018, 22:48

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.

novice07

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

23 Mar 2018, 03:47

1

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.