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Each day after an item is lost the probability of finding that item is

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Bunuel
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Each day after an item is lost the probability of finding that item is [#permalink] New post   20 Sep 2019, 03:28
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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
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Bunuel
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Re: Each day after an item is lost the probability of finding that item is [#permalink] New post   20 Sep 2019, 03:28
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Bunuel 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.

Answer: B.
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Re: Each day after an item is lost the probability of finding that item is [#permalink] New post   20 Sep 2019, 07:24
P of lost 1st day ; 1/x
2nd day ; 1/2x
3rd day ; 1/4x
1/4x=1/64
1/x=1/16
this is P of lost so P of finding item ; 2/16 ; 1/8
IMO B

Bunuel 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
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Re: Each day after an item is lost the probability of finding that item is [#permalink] New post   23 Sep 2019, 13:32
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Solution


Given:
    • Each day after an item is lost the probability of finding that item is halved

To find:
    • If 3 days after a certain item is lost the probability of finding it has dropped to \(\frac{1}{64}\), what was the initial probability of finding the item

Approach and Working Out:
Let the initial probability of finding the item be x
    • After 1 day, it becomes \(\frac{x}{2}\)
    • After 2 days, it will be \(\frac{x}{4}\)
    • After 3 days it is \(\frac{x}{8}\)

Thus, \(\frac{x}{8} = \frac{1}{64}\)

Therefore, x = \(\frac{8}{64} = \frac{1}{8}\)

Hence, the correct answer is Option B.

Answer: B
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Re: Each day after an item is lost the probability of finding that item is [#permalink] New post   29 Sep 2019, 19:30
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Bunuel 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


Since each day after an item is lost the probability of finding that item is halved, then given the probability of that item could be found on a certain day, the probability of finding that item on the prior day must be doubled. Therefore, the initial probability that the item could be found three days prior was 1/64* 2^3 = 8/64 = 1/8.

Alternate Solution:

If p is the initial probability of finding the item, we have p * (1/2) * (1/2) * (1/2) = 1/64; i.e. p/8 = 1/64. Multiplying each side by 8, we find that p = 1/8.

Answer: B
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Re: Each day after an item is lost the probability of finding that item is [#permalink] New post   11 Dec 2023, 00:15
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Re: Each day after an item is lost the probability of finding that item is [#permalink]
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