A drought is a period of abnormal dry weather that causes serious problems in the farming industry of the region. University of Arizona researchers used historical annual data to study the severity of droughts in Texas. (Journal of Hydrologic Engineering, September/October 2003.) The researchers showed that the distribution of x, the number of consecutive years that must be sampled until a dry (drought) year is observed, can be modeled using the formula

Find the probability that exactly 3 years must be sampled before a drought year occurs.

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p(x) = (.7)x-¹(3), x= 1, 2, 3, ...