A basket has 10 mangoes, of which 3 are spoilt. Three mangoes are taken out one after the other without replacement. What is the probability that at least one of them is spoilt?

\frac{1}{120}

Correct answerYour answer

\frac{7}{24}

Correct answerYour answer

\frac{657}{1000}

Correct answerYour answer

\frac{17}{24}

Correct answerYour answer

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CorrectNot quiteAnswer D

Correct answer: D

None spoilt: $\frac{7}{10} \times \frac{6}{9} \times \frac{5}{8} = \frac{7}{24}$ .
At least one spoilt: $1 - \frac{7}{24} = \frac{17}{24}$ .

Worth noting

$\frac{657}{1000} = 1 - \left(\frac{7}{10}\right)^{3}$ puts each mango back before the next one is taken.

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

Explanation