Convective storms occur with probability.7 and magnitude density $f_1(x)=e^{-x}$ for x>0. Cyclone storms have density $f_2(x)=2e^{-2x}$. Find probability magnitude exceeds1,to two decimals.
Interpret the two storm types as exhaustive and mutually exclusive, so cyclone probability is .3. Their exponential survival probabilities at 1 are $e^{-1}$ and $e^{-2}$. Total probability gives $P(X>1)=.7e^{-1}+.3e^{-2}=.2981162$,rounded **.30**. The missing explicit cyclone-type probability is supplied by this two-component-mixture interpretation.
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