P(A) = 2/5, P(B) = 1/4 and P(A B) = 1/10. What is P(A' B)?

Conditional Probability & Bayes' Theorem · Question 12 of 125

Question 12

MediumOriginal question

$P(A) = \frac{2}{5}$ , $P(B) = \frac{1}{4}$ and $P(A \cap B) = \frac{1}{10}$ . What is $P(A' \mid B)$ ?

\frac{1}{10}

Correct answerYour answer

\frac{2}{5}

Correct answerYour answer

\frac{3}{5}

Correct answerYour answer

\frac{3}{4}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$ , and $P(A' \mid B) = 1 - P(A \mid B)$ .
$P(A' \mid B) = 1 - \frac{\frac{1}{10}}{\frac{1}{4}} = \frac{3}{5}$ .

Worth noting

$\frac{2}{5}$ is $P(A \mid B)$ ; the complement within $B$ is $1 - \frac{2}{5}$ .

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

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