Socks in left drawer and right drawer

Dr Evil

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Jan 2, 2018
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A man has different pairs of socks, but the socks are not arranged in pairs. All the right socks are in the right drawer and all the left socks are in the left drawer.
Every day the man pulls out a random sock from the right drawer, then starts pulling socks out of the left drawer, randomly and without rehearsals, until the matching sock is found. Then he wears the pair of socks he doesn't put them back in the drawer.


A. For each day, \(\displaystyle i=1,2,...\) Calculate the probability that the man should have drawn at least 10 socks from the left drawer.


B. For each day \(\displaystyle i=1,2,...\) Calculate the expectation of the number of socks that the man pulled from the left drawer.


C. Consider the total number of socks from the left drawer. Show exact expression and order of magnitude
 
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A man has different pairs of socks, but the socks are not arranged in pairs. All the right socks are in the right drawer and all the left socks are in the left drawer.
Every day the man pulls out a random sock from the right drawer, then starts pulling socks out of the left drawer, randomly and without rehearsals, until the matching sock is found. Then he wears the pair of socks he doesn't put them back in the drawer.


A. For each day, \(\displaystyle i=1,2,...\) Calculate the probability that the man should have drawn at least 10 socks from the left drawer.

B. For each day \(\displaystyle i=1,2,...\) Calculate the expectation of the number of socks that the man pulled from the left drawer.

C. Consider the total number of socks from the left drawer. Show exact expression and order of magnitude

Please show us what work you are able to do, so we can have an idea where you need help. And read the READ BEFORE POSTING message.

Note that this site uses "[ tex]" and "[ /tex]" to mark LaTeX, not dollar signs as you used. I changed that in the quote.
 
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