P(A) = 0.7, P(B) = 0.4 and P(A B) = 0.85. What is P(A B)?

Question 62

MediumOriginal question

$P(A) = 0.7$ , $P(B) = 0.4$ and $P(A \cup B) = 0.85$ . What is $P(A \cap B)$ ?

0.25

Correct answerYour answer

0.28

Correct answerYour answer

0.45

Correct answerYour answer

0.75

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$ , so $P(A \cap B) = P(A) + P(B) - P(A \cup B)$ .
$= 0.7 + 0.4 - 0.85 = 0.25$ .

Worth noting

0.28 multiplies $0.7 \times 0.4$ , which is right only for independent events; nothing here says they are.

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