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The probability that at least one company is going to announce

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Gladiator59
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The probability that at least one company is going to announce [#permalink] New post   10 Mar 2018, 05:18
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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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Re: The probability that at least one company is going to announce [#permalink] New post   10 Mar 2018, 06:37
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
There fore, answer is 60%
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Re: The probability that at least one company is going to announce [#permalink] New post   10 Mar 2018, 06:55
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
There fore, answer is 60%


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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Re: The probability that at least one company is going to announce [#permalink] New post   10 Mar 2018, 07:03
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%
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Re: The probability that at least one company is going to announce [#permalink] New post   10 Mar 2018, 07:05
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Gladiator59 wrote:
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.



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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Thank you for understanding, and happy exploring!
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Re: The probability that at least one company is going to announce [#permalink]
10 Mar 2018, 07:05
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