Bayes's theorem from Tversky and Kahneman in Michael Lewis's The Undoing Project Michael Lewis's book "The Undoing Project" is concerned with the (mathematical) psychologists Daniel Kahneman and Amos Tversky.  (Kahneman won the 2002 Nobel Prize; Tversky died in 1996.)  On page 157, this question is quoted:

The mean IQ of the population of eighth graders in a city is known to be 100.  You have selected a random sample of 50 children for a study of educational achievement.  The first child tested has an IQ of 150.  What do you expect the mean IQ to be for the whole sample.    

Tversky and Kahneman stated: "The correct answer is 101.  A surprisingly large number of people believe that the expected IQ for the sample is still 100" in Psychological Bulletin, vol. 76, 105--110 (1971).  (http://pirate.shu.edu/~hovancjo/exp_read/tversky.htm)  
Can anyone justify the answer of IQ 101?  Is it possible to solve this problem without being given the standard deviation of the population?  

You expect the mean IQ of the remaining $49$ children to be $100$.  Imagine that the first child gives one of his IQ points to each of the remaining $49$ children.  Then we expect the remaining $49$ children have a mean IQ of $101$, and the first child now has an IQ of $101$, so all $50$ children together have a mean IQ of $101$.
