P(A) = 0.4, P(B A) = 0.7 and P(B) = 0.46. What is P(B A')?

Conditional Probability & Bayes' Theorem · Question 88 of 125

Question 88

MediumOriginal question

$P(A) = 0.4$ , $P(B \mid A) = 0.7$ and $P(B) = 0.46$ . What is $P(B \mid A')$ ?

0.18

Correct answerYour answer

0.3

Correct answerYour answer

0.45

Correct answerYour answer

0.54

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

$P(B) = P(A)P(B \mid A) + P(A')P(B \mid A')$ , so $0.46 = 0.4 \times 0.7 + 0.6x$ .
$0.6x = 0.46 - 0.28 = 0.18$ , so $x = 0.3$ .

Worth noting

0.18 is $P(A' \cap B)$ ; it still has to be divided by $P(A') = 0.6$ .

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

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