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Each day after an item is lost the probability of finding th [#permalink]
24 Jan 2011, 03:09

00:00

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Difficulty:

35% (medium)

Question Stats:

63% (01:26) correct
37% (00:35) wrong based on 19 sessions

Each day after an item is lost the probability of finding that item is halved. If 3 days after a certain item is lost the probability of finding it has dropped to 1/64, what was the initial probability of finding the item?

Each day after an item is lost the probability of finding that item is halved. If 3 days after a certain item is lost the probability 1/64, what was the initial probability of finding the item? a)1/32 b)1/8 c)1/4 d)1/2 e)1

Re: Probability: Tricky one [#permalink]
24 Jan 2011, 05:12

Expert's post

gmatpapa wrote:

Each day after an item is lost the probability of finding that item is halved. If 3 days after a certain item is lost the probability of finding it has dropped to \(1/64\) , what was the initial probability of finding the item? \((A) 1/32\) \((B) 1/8\) \((C) 1/4\) \((D) 1/2\) \((E) 1\)

Let the initial probability of finding the item be p then we have that p*(1/2)^3=1/64 --> p=1/8.

Re: Probability: Tricky one [#permalink]
29 Jan 2011, 20:30

gmatpapa wrote:

Yes. the source is Bell Curves.

The part that tricks me is how they've arrived at \(\frac{x^3}{8y^3} = \frac{1}{64}\)

yep, it sure raises doubts. Why do they have to consider the probabilty from the first day. Because the probability for each day becomes half of previous and logically I guess we just have to equate the probability of finding on the THIRD day alone to 1/64.

So then it become as per OE (x/4y) = (1/64) whic will give the initial probability of (1/24), which is not a Answer choice at all

Solving this equation, x = 2.05 or 0.07 or 0.87. The first one can be rejected since probability is always <= 1. So the answer can be either of the remaining two.

I'm sure there's something I'm missing in this problem. It should not involve solving a cubic equation!!

Solving this equation, x = 2.05 or 0.07 or 0.87. The first one can be rejected since probability is always <= 1. So the answer can be either of the remaining two.

I'm sure there's something I'm missing in this problem. It should not involve solving a cubic equation!!

Cheers, Ady

I do believe that if the answer is not 1/8 then the problem is flawed. So leave it. _________________

Originally posted on MIT Sloan School of Management : We are busy putting the final touches on our application. We plan to have it go live by July 15...