I am teaching statistics to high school students. The material we are covering is pretty standard and includes:

• Introducing how to calculate the probability of events, e.g. coin flips, card draws, lottery tickets.

• The sum of the probabilities of all events is $1$

• Independent Events: $P(B \mid A) = P(B)$ and $P(A) \cdot P(B) =P(A \cap B)$

• Venn Diagrams and $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

• Conditional probability: $P(B \mid A) = \frac{P(A \cap B)}{P(A)}$

• Bayes Rule: $P(B \mid A) \cdot P(A) = P(A \mid B) \cdot P(B)$

• Product Rule: $P(B \cap A) = P(A) \cdot P(B \mid A)$

• Total Probability: $P(B) = P(A) \cdot P(B \mid A) + P(\bar{A}) \cdot P(B \mid\bar{A})$

• Binomial Trials

I am looking for examples of common misconceptions students have, or common mistakes that they do, when solving problems. Trivial examples are welcome. A preferred answer should also suggest ways in which one can prevent students to have said misconception.

An example of a common mistake would be:

Problem: You draw a card from a deck. What is the probability that it is red and has value J,Q,K or A?

Answer: $\frac{26}{52} + \frac{16}{52}$

My best suggestion for explaining to a student that this is wrong might be to change the problem to say red and black instead of simply red, and thus following the same logic getting a probability greater than $1$. But having students make similar thoughts seems unrealistic to me, and I am lost at how to best proceed.

I am teaching probability to high school students. The material we are covering is pretty standard and includes:

• Introducing how to calculate the probability of events, e.g. coin flips, card draws, lottery tickets.

• The sum of the probabilities of all events is $1$

• Independent Events: $P(B \mid A) = P(B)$ and $P(A) \cdot P(B) =P(A \cap B)$

• Venn Diagrams and $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

• Conditional probability: $P(B \mid A) = \frac{P(A \cap B)}{P(A)}$

• Bayes Rule: $P(B \mid A) \cdot P(A) = P(A \mid B) \cdot P(B)$

• Product Rule: $P(B \cap A) = P(A) \cdot P(B \mid A)$

• Total Probability: $P(B) = P(A) \cdot P(B \mid A) + P(\bar{A}) \cdot P(B \mid\bar{A})$

• Binomial Trials

I am looking for examples of common misconceptions students have, or common mistakes that they do, when solving problems. Trivial examples are welcome. A preferred answer should also suggest ways in which one can prevent students to have said misconception.

An example of a common mistake would be:

Problem: You draw a card from a deck. What is the probability that it is red and has value J,Q,K or A?

Answer: $\frac{26}{52} + \frac{16}{52}$

My best suggestion for explaining to a student that this is wrong might be to change the problem to say red and black instead of simply red, and thus following the same logic getting a probability greater than $1$. But having students make similar thoughts seems unrealistic to me, and I am lost at how to best proceed.