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You throw four softballs at the strike-zone target shown. The softballs are equally likely to hit any point of the strike-zone target. What is the probability that the first softball hits zone 2, the second softball hits zone 1, the third softball hits zone 3, and the fourth softball hits zone 4?



= ________________(Enter your probability as a fraction.) 





 Oct 1, 2018

\(\text{The strike zone looks to be }18 \times 24 = 432~sq~in \text{ in area}\\ \text{each of the triangles is }\dfrac{6^2}{2} = 18~sq~in~\text{in area} \\ \text{Thus the probability of hitting any of those triangles is }\\ p=\dfrac{18}{432} = \dfrac{1}{24}\)


\(\text{The throws are independent so we just multiply the individual probabilities together to}\\ \text{get the probability of all 4 events occurring}\\ p = \left(\dfrac{1}{24}\right)^4 = \dfrac{1}{331776}\)

 Oct 1, 2018

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