If I have a 1/3 chance of winning in five competitions, how likely is it that I would win at least once? I have tried 1/3 to the power of 5.
+33616 The probability that you wouldn't win at all is (2/3)5, so the probability you would win at least once is 1 - (2/3)5
$${\mathtt{p}} = {\mathtt{1}}{\mathtt{\,-\,}}{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{5}}} \Rightarrow {\mathtt{p}} = {\mathtt{0.868\: \!312\: \!757\: \!201\: \!646\: \!1}}$$
(1/3)5 gives the probability that you win in all five competitions!
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+33616 The probability that you wouldn't win at all is (2/3)5, so the probability you would win at least once is 1 - (2/3)5
$${\mathtt{p}} = {\mathtt{1}}{\mathtt{\,-\,}}{\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}^{{\mathtt{5}}} \Rightarrow {\mathtt{p}} = {\mathtt{0.868\: \!312\: \!757\: \!201\: \!646\: \!1}}$$
(1/3)5 gives the probability that you win in all five competitions!
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