Conditional Probability and Independent Events

Statistics — Third Secondary

Common mistakes

Comparison aspect	Main idea	Keywords
Dividing by P(A) instead of P(B)	in P(A \| B) the denominator is the probability of the conditioning event B	denominatorprobabilityconditioningevent
Confusing independence with mutual exclusiveness	mutually exclusive events cannot occur together while independent events can occur together	mutuallyeventscannotoccur
Assuming independence without testing	check that P(A ∩ B) = P(A) × P(B) before deciding	checkbeforedeciding
Forgetting that the sample space changes without replacement	the total number of balls changes after each draw	totalnumberballsafter
Thinking that P(A \| B) = P(B \| A)	the two probabilities are usually different	probabilitiesusuallydifferent

Conditional Probability and Independent Events · 6 / 7