Tuesday, February 17, 2009

BRAINTENANCE QUIZ 2/17/09

Dear Friends:

Firstly, here are the answers to our last challenge (a.k.a. the "St. Valentine's Day Massacre"):

Situation: A young man (who takes "enhancement" supplements, and believes in portfolio diversification theory) has purchased five valentines cards, each with an envelope, to send out to his five current girlfriends. He writes a personal note on each of the cards (writing each of the young lovelies by name, and saying that she is 'the only one for me'), and addresses the envelopes.

He is distracted by a knock on the door (probably his landlady, whom he pays in services in lieu of currency), and he sweeps the letters and the envelopes to the floor. After rendering the services to the landlady, he is dazed and confused. He rapidly stuffs cards into the envelopes, without being too careful.

Two cards wound up in the wrong envelopes -- each of these receipients will get the card intended for another. He stamps them and posts them.

Questions: Without rendering a moral judgment regarding the potentially lethal mistake that he has made:

What is the probability that any one of the young ladies in his stable will receive the wrong card?
This question is an easy one to answer. We know that two women will be reciving the wrong cards. Any two young ladies out of five young ladies in total, is 2 divided by 5, or 40% ...a .40 probability. The probability of any woman getting the wrong card is 40%. Our Lothario is in deep trouble.

What is the probability that any one of the young ladies will recieve the right card (phew)?
Since the probability of any young lady receiving the wrong card is 40%, as we have just demonstrated. Since any of the young ladies can either receive a "right" card or a "wrong" card, the probability of any young lady receiving a "right" card is 1.00 - .40, or .60. The probability of any one of the young ladies receiving a "right" card will be .60, or 60%.
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And now, for today's puzzle:

1. Given the same circumstances above, and the same rate of confusion as above, if a similar (and equally ambitious but careless) young man starts off with 100 young ladies, and makes this mistake 4 years in succession, and assuming that he does not add any new ladies to his portfolio, or win any deceived and hurt young ladies back, despite his charms and creative excuses, how many young ladies will remain available to him at the end of four fateful Valentine's Day debacles?

2. TONGUE TWISTER: A box of biscuits, a batch of mixed biscuits.

3. TONGUE TWISTER: A skunk sat on a stump and thunk the stump stunk, but the stump thunk the skunk stunk.

Note: Tongue twisters are not only helpful for people in speech therapy (or as an indication of the toxicity level of alcohol in someone's bloodstream) -- they force us to think about the nature of what we are actually saying in order to avoid the obvious slip-ups. Tongue twisters heighten our awareness of what we are reading and of what we are saying.

Faithfully,

Douglas Castle