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05 Jul 2018, 04:50
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Difficulty:
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Question Stats:
72% (01:53) correct
28%
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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. \(\frac{6}{7}\)
A. \(\frac{1}{1400}\)
B. \(\frac{1}{600}\)
C. \(\frac{1}{7}\)
D. \(\frac{1}{2}\)
E. \(\frac{6}{7}\)
05 Jul 2018, 05:53
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Bunuel
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)
05 Jul 2018, 06:15
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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
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
