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# The probability that a sleeper bomb will blow up in any

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Founder
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The probability that a sleeper bomb will blow up in any [#permalink]  19 Jun 2003, 01:31
Expert's post
The probability that a sleeper bomb will blow up in any given year is 5%.

If there is a sleeper bomb sitting in one of the canyons in the city of Monrovia what is the probability that it will blow up this year if it has been sitting there already for 10 years?
Manager
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I don┬┤t understand the question, but if each year is independent to the other, I mean if each year has a 5% probability no matter how many years, then the prob is 5% like any other year (it seems too easy)

Can you explain the question
thanks
Founder
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Expert's post
OK, my mistake. Let me rephrase the problem:

The probability that a sleeper bomb will blow up in any given year is 5%.

If there is a sleeper bomb sitting in one of the canyons in the city of Monrovia what is the probability that it will blow up this year if it has been sitting there already for 10 years and no sleeper bomb has ever lasted more than 20 years without blowing up?

P.S. I thought it would be clear from the 5% deal that it will last for 20 years, but it is not; I am sorry about that. Basically the life of the bomb is 20 years - it will for sure blow up at the end of that time.
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The probability is 10%

The bomb will last ten years more at most and therefore the probability of it going off in any of the next ten years is 1/10 = 10%
Manager
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I agree with prashant it has to be a 10%

If I have a 20 year period, then I have a 5% probability in each year. If time is reduced to ten years, then prob increases to 10%.
Manager
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If it is true that odds of blowing up of the bomb increases every year by the percent of remaining yers , then % of blowing up the bomb in 11th year is 100/9 = 11.11 ( Bomb did not blow up in the past 10 years )

_________________

Brainless

Founder
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Expert's post
Hm... I personally thought it would be adding up when I was coming up with the problem. I wonder if there is a case when probability would add up? Any ideas?
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brainless:

the probability is 1/9=11.11% if you assume that you are at the end of the 11th year. But if you are at the beginning of the 11th year, then the probability of the bomb going off in that year is 1/10=10%

bb: the probabilities are additive because

(the bomb goes off in 11th year) OR (in 12th year) OR.... etc.
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