What is P(E F)?

Question 19

MediumOriginal question

Two fair dice are thrown. $E$ : the sum is 9. $F$ : at least one die shows a 5.

What is $P(E \mid F)$ ?

\frac{1}{18}

Correct answerYour answer

\frac{1}{6}

Correct answerYour answer

\frac{2}{11}

Correct answerYour answer

\frac{1}{2}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$F$ has 11 outcomes: 6 with the first die 5, 6 with the second die 5, less $(5, 5)$ counted twice.
Of these, $(4, 5)$ and $(5, 4)$ sum to 9: $\frac{2}{11}$ .

Worth noting

$\frac{1}{6} = \frac{2}{12}$ counts $(5, 5)$ twice when listing $F$ .

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

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