Last visit was: 25 May 2024, 00:42

It is currently 25 May 2024, 00:42

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Go to My Error Log Learn more

Request Expert Reply

Confirm Cancel

PREVIOUS TOPIC

NEXT TOPIC

Probability that at least one of the event occurs is ?

novice07

Intern

Joined: 20 Mar 2018

Posts: 39

Own Kudos [?]: 125 [0]

Given Kudos: 0

GRE 1: Q163 V149

GRE 2: Q168 V162

GPA: 3.5

Send PM

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

10 Apr 2018, 01:37

https://gre.myprepclub.com/forum/qotd-19-f ... tml#p18435
A similar question with official explanation

mohan514

Manager

Joined: 26 Jan 2018

Posts: 189

Own Kudos [?]: 165 [0]

Given Kudos: 0

GRE 1: Q165 V156

Send PM

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

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

cyanApples

Intern

Joined: 19 Mar 2018

Posts: 14

Own Kudos [?]: 12 [0]

Given Kudos: 0

Send PM

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

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.

Posted from my mobile device

mohan514

Manager

Joined: 26 Jan 2018

Posts: 189

Own Kudos [?]: 165 [0]

Given Kudos: 0

GRE 1: Q165 V156

Send PM

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

11 Apr 2018, 09:25

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

Sissa14

Intern

Joined: 05 Mar 2018

Posts: 3

Own Kudos [?]: 1 [0]

Given Kudos: 0

Send PM

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

03 May 2018, 16:50

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

halam

Intern

Joined: 14 Apr 2018

Posts: 7

Own Kudos [?]: 14 [0]

Given Kudos: 0

Send PM

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

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?

mohan514

Manager

Joined: 26 Jan 2018

Posts: 189

Own Kudos [?]: 165 [0]

Given Kudos: 0

GRE 1: Q165 V156

Send PM

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

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.

Posted from my mobile device

Important thing to be noted. Probability of any event happening ranges between 0 and 1. Probability cannot have value beyond this range.

KarunMendiratta

Retired Moderator

Joined: 16 Apr 2020

Status:Founder & Quant Trainer

Affiliations: Prepster Education

Posts: 1546

Own Kudos [?]: 2972 [0]

Given Kudos: 172

Location: India

WE:Education (Education)

Send PM

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

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 \( 0.5\)