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

Question

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

A. 1/32
B. 1/8
C. 1/4
D. 1/2
E. 1

Bunuel · Answer

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.

Archit3110 · Answer

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

EgmatQuantExpert · Answer

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

ScottTargetTestPrep · Answer

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

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