Conjunction fallacy occurs when people believe that the co-occurrence of two events is more likely than the occurrence of one of the events alone, despite the fact that the probability of two events occurring together is always lower than the probability of either event occurring alone.
For example there is a question and two options: something that happens rarely, 12% of the time, and something that happens often, 80% of the time. However, when the more likely option is presented, our minds become fixated on it, much like a child fixated by a glowing lollipop. We lose sight of the fact that when the less likely option is presented alongside the more likely one, it has a lower chance of occurring, at only 9.6% (12% * 80%), compared to when it is presented alone at 12%.
The conjunction fallacy also occurs when the second option associates us with the profile of what we are trying to find. For example Katy was a student, who was deeply concerned with issues of social justice, and also participated in anti-discrimination demonstrations. Which is more probable? Katy is a bank teller or Katy is a bank teller and is active in the feminist movement.
This may be related to
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.