A and B are independent with P(A) = 1/4 and P(B) = 2/5. What is the probability that neither happens?

Conditional Probability & Bayes' Theorem · Question 54 of 125

Question 54

EasyOriginal question

$A$ and $B$ are independent with $P(A) = \frac{1}{4}$ and $P(B) = \frac{2}{5}$ . What is the probability that neither happens?

\frac{9}{20}

Correct answerYour answer

\frac{11}{20}

Correct answerYour answer

\frac{3}{5}

Correct answerYour answer

\frac{3}{4}

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CorrectNot quiteAnswer A

Correct answer: A

$A'$ and $B'$ are independent too: $P(A' \cap B') = \frac{3}{4} \times \frac{3}{5}$ .
$= \frac{9}{20}$ .

Worth noting

$\frac{11}{20}$ is the chance that at least one happens, $1 - \frac{9}{20}$ .

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

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