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

Conditional Probability & Bayes' Theorem · Question 87 of 125

Question 87

MediumOriginal question

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

0.3

Correct answerYour answer

0.4

Correct answerYour answer

0.5

Correct answerYour answer

0.6

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$A$ and $A'$ split the sample space: $P(B) = P(A)P(B \mid A) + P(A')P(B \mid A')$ .
$0.5 \times 0.4 + 0.5 \times 0.2 = 0.3$ .

Worth noting

0.6 adds the two conditional probabilities without weighting them by $P(A)$ and $P(A')$ .

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

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