The conjunction fallacy (aka the Linda problem) occurs when an arguer mistakes a conjunction (an "and" statement) to be more likely true than one of its conjuncts (one side of the "and"). The mistake usually stems from the conjunction seeming more representative of the subject.
Here is a version of the classic example:

Linda is in her 30's, has a Humanities degree, reads social criticism, and is interested in social justice causes. Which of these two statements is more likely to be true: 1. Linda is a bank teller. 2. Linda is a bank teller and a feminist.
Many people will mistakenly pick #2. It is not the most likely, because it already contains condition #1, plus demands more. Even if there is only a 1% chance of Linda not being a feminist, that makes statement #2 at least slightly less likely than #1.
A general template of this fallacy would be:
1. Attribute G seems likely to represent person (or thing) A:
2. Therefore "A is both F & G" is more likely to be true than "A is F" is.
Reference: Tversky, Amos; Kahneman, Daniel (October 1983). "Extension versus intuitive reasoning: The conjunction fallacy in probability judgment". Psychological Review. 90 (4): 293–315.