A problem is given to two students, who solve it independently with probabilities 1/2 and 1/3. What is the probability that the problem is solved?

Conditional Probability & Bayes' Theorem · Question 53 of 125

Question 53

EasyOriginal question

A problem is given to two students, who solve it independently with probabilities $\frac{1}{2}$ and $\frac{1}{3}$ . What is the probability that the problem is solved?

\frac{1}{6}

Correct answerYour answer

\frac{1}{3}

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\frac{2}{3}

Correct answerYour answer

\frac{5}{6}

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The problem stays unsolved only if both fail: $\frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$ .
$1 - \frac{1}{3} = \frac{2}{3}$ .

Worth noting

$\frac{5}{6}$ adds the two chances, counting twice the case where both solve it.

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

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