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# A certain bank vault contains 600 safe deposit boxes. A thief possesse

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A certain bank vault contains 600 safe deposit boxes. A thief possesse  [#permalink]

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05 Jul 2018, 03:50
00:00

Difficulty:

45% (medium)

Question Stats:

66% (02:03) correct 34% (01:47) wrong based on 80 sessions

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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. $$\frac{6}{7}$$

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Re: A certain bank vault contains 600 safe deposit boxes. A thief possesse  [#permalink]

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05 Jul 2018, 04:53
Bunuel wrote:
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. $$\frac{6}{7}$$

There are $$C_1^{600}$$ or 600 ways of choosing a certain safe deposit box.
Similarly, there are $$C_1^{700}$$ or 700 ways of choosing a key to open the box.

To open the box, the thief must choose the corresponding 300 boxes for which he has the keys.

Therefore, the probability that the thief will be able to open the box is $$\frac{1*300}{600*700} = \frac{1}{1400}$$(Option A)
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A certain bank vault contains 600 safe deposit boxes. A thief possesse  [#permalink]

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05 Jul 2018, 05:15
1
First we have to choose a box, we need to choose from those 300 boxes for which the thief has the keys, so the probability is $$\frac{300}{600}$$
AND
then we need to choose exactly the right 1 key to open that box $$\frac{1}{700}$$.
In probability questions AND means multiplication so we get $$\frac{300}{600}*\frac{1}{700}=\frac{1}{1400}$$

If we had to select first the key and then the box:
$$\frac{300}{700}$$ the probability that we choose the key that will definitely open one of the boxes
AND
$$\frac{1}{600}$$ the probability that we'll choose exactly the right box for our chosen key
$$\frac{300}{700}*\frac{1}{600}=\frac{1}{1400}$$

In My opinion
Ans: A
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Re: A certain bank vault contains 600 safe deposit boxes. A thief possesse  [#permalink]

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09 Jul 2018, 18:59
Bunuel wrote:
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. $$\frac{6}{7}$$

First, he has a 300/700 = 3/7 chance to pick a key that can open any one of the safe deposit boxes. After he picks a key that can open a safe deposit box, he has 1/600 chance to pick the right safe deposit box. Thus, the probability is 3/7 x 1/600 = 1/7 x 1/200 = 1/1400.

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Re: A certain bank vault contains 600 safe deposit boxes. A thief possesse  [#permalink]

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10 Jul 2018, 08:13
Let's first find the total number of possible results: we have 700 keys on one side, and 600 boxes on the other, so we have 600*700 possible combinations.

We have 300 desired results, which are the keys that open a box.

The probability is then 300/(600*700) = 1/1400.
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Re: A certain bank vault contains 600 safe deposit boxes. A thief possesse &nbs [#permalink] 10 Jul 2018, 08:13
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