Which of the following statements are true?
I. If $A$ and $B$ are independent, so are $A'$ and $B'$ .
II. Two mutually exclusive events with positive probabilities are independent.
III. If $A$ and $B$ are independent, $P(A \mid B) = P(A)$ .
IV. If $A$ and $B$ are independent, $P(A \cap B) = P(A)\,P(B)$ .

All four: I, II, III and IVCorrect answerYour answerI, III and IV onlyCorrect answerYour answerIII and IV onlyCorrect answerYour answerII, III and IV onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

I, III and IV hold for independent events.
II is false: mutually exclusive means $P(A \cap B) = 0$ , but $P(A)\,P(B) > 0$ .

Worth noting

Exclusive events are as dependent as can be: if one happens, the other cannot.

Concept: Independence and exclusiveness
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsIndependent events

Practise this chapter →

Ten questions from Conditional Probability & Bayes' Theorem, at your own pace.

Explanation