1) Giving answers to probabilities that don't make sense.
~Probabilities are always numbers between 0 & 1, inclusively.
~They can be expressed as decimals, fractions, or percentages.

2)  Giving a probability when a question is calling for odds.
~An answer for odds gives a whole number to a whole number where the first whole number is larger. Also, specifying  that the odds are in favor or against.

3)  Trying to use a complicated or an involved method of computing a probability when all that is needed is the basic definition.
~The basic definition can be used to solve most problems encountered in an introductory course.

4)  Failing to subtract the probability of the intersection of two events when using the addition (OR) rule with events that can occur simultaneously.
~If the two events are mutually exclusive, there is no subtraction, simply add their probabilities.  However, if they are not mutually exclusive, you must subtract P(A and B) from the sum of P(A) & P(B).

5)  When using the backdoor approach, the complement of the event is not figured properly.
~The backdoor approach is a valuable method of computing the P(A) indirectly by subtracting the P(not A) from one. Along with an error in figuring the complement, many students forget to subtract P(not A) from one.
~There are many problems that cannot be solved directly & this method must be used. A very important approach for computing a probability.

6)  Not considering whether or not probabilities of multiple events are computed with or without replacement.
~Answers come out different in these cases.  Not replacing an object after it is selected changes the size of the sample space for the next selection, consequently, its probability.

7)  Misreading data from a contingency table.
~Each cell of a contingency table is the intersection of the data indicated in the column heading with the data the row is indicating.

8) Failing to change the sample space in conditional probability.
~For P(A|B), event B has occurred. We would like to compute P(A) under that circumstance. The new sample space used for computing P(A) is the sample space for B.