2010016905 | math4u.vsb.cz

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2010016905

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There are sixty apples left on a tree and twelve of them have worms. We pick six apples at random. What is the probability that at least one of them is without a worm?

1 - \frac{(\binom{12}{6})}{(\binom{60}{6})} ≐ 0.999982

1 - \frac{(\binom{12}{1})}{(\binom{48}{6})} ≐ 0.999999

1 - \frac{(\binom{12}{1}) \cdot (\binom{48}{5})}{(\binom{60}{6})} ≐ 0.589571

\frac{(\binom{12}{1}) + (\binom{12}{2}) + (\binom{12}{3}) + (\binom{12}{4}) + (\binom{12}{5})}{(\binom{60}{6})} ≐ 0.000032