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

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Re: Each day after an item is lost the probability of finding that item is [#permalink]
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

$$\frac{1}{8} ----> \frac{1}{16} ---->\frac{1}{32} ---->\frac{1}{64}$$

Hence, the correct answer to the above question will be (B) $$\frac{1}{8}$$
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Re: Each day after an item is lost the probability of finding that item is [#permalink]
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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

We are given that each day after an item is lost, the probability of finding that item is halved, and that 3 days after the item is lost, the probability of finding it has dropped to 1/64.

We can let the initial probability of finding the item = x

Thus, after day 1, the probability is (1/2)x, after day 2 it’s (1/4)x, and after day 3 it’s (1/8)x.

We can set (1/8)x equal to 1/64 and we have:

(1/8)x = 1/64

Multiply both sides by 8, we have:

x = 1/8

The initial probability of finding the item was 1/8.

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Re: Each day after an item is lost the probability of finding that item is [#permalink]
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Re: Each day after an item is lost the probability of finding that item is [#permalink]
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