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A certain bank vault contains 600 safe deposit boxes. A thie

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A certain bank vault contains 600 safe deposit boxes. A thie [#permalink] New post 27 Mar 2018, 10:08
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66% (01:33) correct 33% (01:54) wrong based on 6 sessions
A certain bank vault contains 600 safe deposit boxes. A thief possesses a sack containing 700 keys, only 300 of which correspond to the safe deposit boxes, with no duplicates. If the thief randomly selects a box and then a key, what is the probability that the thief will be able to open the box?



A. \(\frac{1}{1400}\)

B. \(\frac{1}{600}\)

C. \(\frac{1}{7}\)

D. \(\frac{1}{2}\)

E. \(\frac{6}{7}\)
[Reveal] Spoiler: OA

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Re: A certain bank vault contains 600 safe deposit boxes. A thie [#permalink] New post 27 Mar 2018, 12:35
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These answers look like they're written in Aztec and my Aztec is pretty rusty, but I'll just solve the problem anyway.

We can look at this problem as finding the probability that 2 events both happen. For example, the probability that you roll two 6s on two dice is 1/6 on the first die, and 1/6 on the second die, and if you multiply 1/6 by 1/6 you get 1/36, which is the odds that both 6s happened.

In this case, the two events are:
1) the odds he picks a safe deposit box which matches one of the 300 keys he's got. Since there are 600 boxes and he's only got in his bag keys for 300 of them, the odds he picks a box matching a key is 1/2.

2) the odds that the key he grabs matches the box he picked. The fact that 400 keys don't match any box is irrelevant. All that matters is he's got 700 keys and only one of them matches this box he's looking at. So the odds the key matches are 1/700.

Finally, we need to multiply 1/2 by 1/700 to get his odds of success, giving us 1/1400 for the answer.
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Re: A certain bank vault contains 600 safe deposit boxes. A thie   [#permalink] 27 Mar 2018, 12:35
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