Read the two statements and choose the correct option. I. P(A A) = 1 whenever P(A) > 0. II. P(A B) = P(B A) for any two events.

Conditional Probability & Bayes' Theorem · Question 11 of 125

Question 11

MediumOriginal question

Read the two statements and choose the correct option.
I. $P(A \mid A) = 1$ whenever $P(A) > 0$ .
II. $P(A \mid B) = P(B \mid A)$ for any two events.

Only ICorrect answerYour answerOnly IICorrect answerYour answerBoth I and IICorrect answerYour answerNeither I nor IICorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

I: $\frac{P(A \cap A)}{P(A)} = 1$ . True.
II is false: the two divide the same $P(A \cap B)$ by different numbers, $P(B)$ and $P(A)$ .

Worth noting

Swapping the condition changes the denominator.

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

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