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# The probability that at least one company is going to announce

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Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 670
The probability that at least one company is going to announce  [#permalink]

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10 Mar 2018, 04:18
1
00:00

Difficulty:

(N/A)

Question Stats:

20% (01:15) correct 80% (00:48) wrong based on 5 sessions

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The probability that at least one company is going to announce a takeover in the next hour is 84%. What is the probability that at least one announces in the next 30 minutes? ( assuming that the distribution of announcement time is independently uniformly distributed )

A) 40%
B) 42%
C) 56%
D) 60%
E) 84%

Source : Other - Brilliant.

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Joined: 06 Mar 2018
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Re: The probability that at least one company is going to announce  [#permalink]

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10 Mar 2018, 05:37
Since distribution of announcement time is independently uniformly distributed
The number of distributions per hour has mean λ and is Poisson
p(X≥1)=1−p(X=0)=1−e^(−λ)=0.84
⟹λ=−ln0.16
So, the probability of announcement in 30 minutes is
1−e(-30λ/60)=1−e^ln0.4=0.6
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 670
Re: The probability that at least one company is going to announce  [#permalink]

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10 Mar 2018, 05:55
swetakumari wrote:
Since distribution of announcement time is independently uniformly distributed
The number of distributions per hour has mean λ and is Poisson
p(X≥1)=1−p(X=0)=1−e^(−λ)=0.84
⟹λ=−ln0.16
So, the probability of announcement in 30 minutes is
1−e(-30λ/60)=1−e^ln0.4=0.6

I am not sure I completely understand the math being used in there. Can you elaborate the steps used a bit further?

Thank you for posting!
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“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)

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Joined: 14 Nov 2014
Posts: 632
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
The probability that at least one company is going to announce  [#permalink]

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10 Mar 2018, 06:03
Hi Bunuel
i am not sure , if the approach is correct ...but i got the answer
Probability of not announcing in a hour = 1-84/100 = 16 /100
in 2 time interval(30 min each ) = P^2 (prob of not announcing in 30 min each)= 16/100 = 4/10
so announcing will be 1-4/10 = 6/10 = 60%
Math Expert
Joined: 02 Sep 2009
Posts: 52361
Re: The probability that at least one company is going to announce  [#permalink]

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10 Mar 2018, 06:05
The probability that at least one company is going to announce a takeover in the next hour is 84%. What is the probability that at least one announces in the next 30 minutes? ( assuming that the distribution of announcement time is independently uniformly distributed )

A) 40%
B) 42%
C) 56%
D) 60%
E) 84%

Source : Other - Brilliant.

___________________
Not a GMAT question.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: The probability that at least one company is going to announce &nbs [#permalink] 10 Mar 2018, 06:05
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