National Sock Day

National Sock Day

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Today is dedicated to celebrate the rarest of all lasting unions (actually if I keep these up it might be ours), the marriage of matched socks, which if they manage to find each other, wash after wash, dry after to dry, through the space and time continuum is (at least in our household) truly remarkable.  This is a mystery someone should really study because despite our best efforts I am always struggling to match socks. We have a bag that will put our single socks in and once in a while I will dump it out and sort through it to get a few pairs.  Apparently this exercise is used to teach kids (exactly what I am not sure) but I am not alone in my pleasure to match socks https://www.youtube.com/watch?v=Fye-b_iRQPM .  So lets see how many of you can pass my sock matching test – in your laundry basket you have 12 white and 12 dark socks – what is the probability of you picking two black socks at random out of the basket?

Well that’s it folks. Oops, almost forgot the answer to the sock matching test.  Well if you said 50% you would be wrong!  You see once you take a sock out of the basket the odds change for the next selection (it becomes asymmetrical) – let me show you

The first draw 12 vs 12 is symmetrical therefore the odds are 12/24 = ½ or 50% – so say you pick a Black or White sock the chance of picking another is different …. as there are 11 black socks and 12 white ones or 12 black ones and 11 white ones depending upon what you picked – the symmetry no longer exists therefore the probability of picking a matching socks is = (½ ) x (11/23) which wait for it we are still not done because the probability of picking a white pair is equal to picking a black pair initially therefore the formulas for picking a pair of matching socks (white or black) is (½ ) x (11/23) + (½ ) x (11/23) = 11/23 =47.8% Don’t believe me – watch this https://www.youtube.com/watch?v=wjsG2Os0–o  isn’t math fun.  If you want to challenge your brain some more watch this https://www.youtube.com/watch?v=uCsD3ZGzMgE (yes I am a complete Nutter!)

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