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Question Number 173842 by byaw last updated on 19/Jul/22

$$$$ The probability that an athlete will not win any of the three races is 1/4. If the athlete runs in all the races, what is the probability that the athlete will win: (I) only the second race: (ii) all the three races (iii) only two of the races?\n

Answered by mr W last updated on 20/Jul/22

$$saytheprobabilitythathewinsa$$ $$raceisp.itisgiven$$ $${(1-p)}^3=\frac{1}{4}$$ $$\Rightarrow p=1-\frac{1}{\sqrt[3]{4}}=0.37$$ $$\left(i\right)$$ $$0.63\times 0.37\times 0.63=0.146=14.6\mathrm{\%}$$ $$\left(ii\right)$$ $$0.{37}^3=0.05=5\mathrm{\%}$$ $$\left(iii\right)$$ $$3\times 0.{37}^2\times 0.63=0.259=25.9\mathrm{\%}$$

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