The Representative Fallacy:(R)

This is a commonly held misconception about probability that states that one event is more likely than another just because it appears more representative of a typical element of the sample space. Here's a familiar example: What is more likely to win the UK National Lottery; {1,2,3,4,5,6} or {4,11,23,31,37,41}? Our intuition tells us that you'd be crazy to pick the first set of numbers - they seem so unusual - but they are just as likely as the other set.

(The UK National Lottery is a 6/49 system - you have to correctly pick 6 numbers drawn at random without replacement from the numbers 1 through 49. Many lotteries in other countires have very similar systems. You'll be familiar with the types of superstition and 'schemes' people have for winning. Read Matthew Ferguson's story, and visit www.smartluck.com for an easy way to win millions!(?))

An excerpt from Darrel Huff's excellent book "How to take a chance":

The story of the Pitosfky family: (R)

In more than a century, seven generations of the Pitofsky family have produced only sons. In 1959 the forty-seventh consecutive boy in the line was born to Mr and Mrs Jerome Pitofsky of Scarsdale NY, or so the New York Times reported. Assuming no overlooked girls and no distortions of the record in the interests of a marvel, this is a one-chance-in 136 trillion (A US trillion equals a British billion) occurrence. While pondering its significance, you may want to consider this: the pattern of the last forty-seven births in YOUR family is also one that would occur just once in 136 trillion times...on the average.

What happened when David Harris checked his order list at IST, August 1999:(R)

I was checking off a long list of books and other equipment that I had ordered for school in the D and T workshop, which was at that time completely empty. I couldn't find one item on the list , and my eye made several 'scans' of the list of items with no result. I lost patience and thought "Oh well, I suppose it is not there". An instant later, I found the item - right at the top of the page! Subconsciously, I judged that I was more likely to find the item somewhere in the middle 75% or so of the list. The mistake I made was that the individual item was just as likely to appear in any position - top, bottom or any other place. All this despite my "Firm grasp" of probability..................

The coincidence of Richard Matthews' wife:

Richard's wife, Adriana, is Columbian. She has three children, two of whom are twins. She met another Columbian woman here in Toulouse. She also has twins - born on the exact same day that Adriana's were born!

(How could you find the probability of Adriana meeting such a woman? What types of events are there in this story? What information would you need to do so? How exact would your answer be?)