P(A C) = 0.5, P(B C) = 0.4 and P(A B C) = 0.2. What is P(A B C)?

Conditional Probability & Bayes' Theorem · Question 7 of 125

Question 7

EasyOriginal question

$P(A \mid C) = 0.5$ , $P(B \mid C) = 0.4$ and $P(A \cap B \mid C) = 0.2$ . What is $P(A \cup B \mid C)$ ?

0.3

Correct answerYour answer

0.7

Correct answerYour answer

0.8

Correct answerYour answer

0.9

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Given $C$ , the addition rule holds as usual: $P(A \cup B \mid C) = P(A \mid C) + P(B \mid C) - P(A \cap B \mid C)$ .
$0.5 + 0.4 - 0.2 = 0.7$ .

Worth noting

0.9 adds the two conditional probabilities and so counts the overlap $A \cap B$ twice.

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

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