Editing Conjunction fallacy (section)

===  Tversky & Kahneman (1983) ===

Tversky and Kahneman followed up their original findings with a 1983 paper<ref name="tk83"/> that looked at dozens of new problems, most of these with multiple variations. The following are a couple of examples.

<blockquote>Consider a regular six-sided die with four green faces and two red faces. The die will be rolled 20 times and the sequence of greens (G) and reds (R) will be recorded. You are asked to select one sequence, from a set of three, and you will win $25 if the sequence you choose appears on successive rolls of the die.

# RGRRR
# GRGRRR
# GRRRRR</blockquote>

65% of participants chose the second sequence, though option 1 is contained within it and is shorter than the other options. In a version where the $25 bet was only hypothetical the results did not significantly differ. Tversky and Kahneman argued that sequence 2 appears "representative" of a chance sequence<ref name="tk83"/> (compare to the ''[[clustering illusion]]'').

<blockquote> 
A health survey was conducted in a representative sample of adult males in British Columbia of all ages and occupations.
    
Mr. F. was included in the sample. He was selected by chance from the list of participants.

Which of the following statements is more probable? (check one)

# Mr. F. has had one or more heart attacks.
# Mr. F. has had one or more heart attacks and he is over 55 years old.</blockquote>

The probability of the conjunctions is never greater than that of its conjuncts. Therefore, the first choice is more probable.