Note: Here, at last, are the promised answers to the mind-bender of February 15th, which were promised by February 19th, and which deadline was further extended because of a temporary mind loss...now, it's (ulp) February 23rd.
An Issue of Sanitation and Speculation - Braintenance
Note: A most unusual posting where we combine observed bathroom antics and public health with probability.
Only at http://Braintenance.blogspot.com
Dear Fellow Intellectual Elitists (some of whom are brilliant, and a few of which are self-defensively delusional) and Brain Barrier Busters:
It has been determined after many years of observation, study and statistical analysis, that only 1 in 8 males actually washes his hands immediately after using the restroom and prior to his exit. Knowing this disenchanting factoid, please answer the following questions:
1. If you are outside of the restroom (for whatever reason), and you are compelled by social obligation to shake hands with every individual who exists the restroom after having "done his thing," what is the probability (in terms of a percentage) that the first person whose hand you shake will have (whew!) washed his hands? The probability is a simple one in eight, one eighth, or (expressed as a percentage) 12.5%.
2. In the same circumstances as in 1), above, what is the probability that the third person whose hand you shake will have washed his hands? The probability will still be 12.5%, as each man's handwashing protocol is independent of next...at least if they are not watching eachother...
3. If you shake hands with eight of these chaps in succession, what is the probability that you will have shaken the hand of any one person who will have washed his hands? Since the probability that you will have had the pleasure of shaking hands with one of these obsessive-compulsive fastidiously clean fellows-well-met (or fellows not -wet) is 87.5%, but you have to shake hands with all of these fellows (eight of 'em), you have to do a bit of cogitation:
Firstly, the question being asked is actually "what is the likelihood that you will shake the hand of one person (the likelihood being .125) who has actually washed his hands?" The likelihood of your shaking the hand of one of the "traditionalists" (i.e., zip it and run) is .875.
If you are shaking the hands of all eight of these superstars, it does not guarantee that one will actually be a hand washer. We are dealing in probability and not certainty. Remember, there is a measurable probability that four of the eight have washed their hands just as there is some probability that not a single one of the eight has washed post-jostle...
Taking it a step at a time, and knowing that each of these deodorant cake refracting chums has an independent probability of being a hand washer, we put together a long multiplication chain, of the independent probabilities in each case, and assume that one fellow is the sanitary 12.5%-er, and the others, each, are 12.5%-ers. Let's assume (since order doesn't matter) that the first fellow is a "clean one," and that all of the seven to follow are representatives of the "unwashed masses".
(.125)x(.875)x(.875)x(.875)x(.875)x(.875)x(.875)x(.875) = .0490868 = 4.91% (approximately).
4. If you know that the person whom you have just shaken hands with was a non-washer, what is the probability that the next person emerging from the lavoratory will be a non-washer as well? It's still going to be 87.5%.
5. If you decide to become adventurous and wear gloves during every handshake for the first seven of eight successive handshakes, what is the likelihood that you will have shaken hands with a hand-washer when your gloves were off? Refer back to question #3, and its answer. The gloves are just a distraction...they do not effect the probability of these separate, independent events.
It's February 15th. I'll have answers for you by February 19th at latest. I over-promised and under-delivered.
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