The total number of hours, measured in units of100 hours, that a family runs a vacuum cleaner over aperiod of one year is a continuous random variable Xthat has the density function f(x)=\left\{\begin{array}{ll}

x, & 0

2-x, & 1 \leq x<2 \\

0, & \text { elsewhere. }

\end{array}\right. Find the probability that over a period of one year, afamily runs their vacuum cleaner (a) less than 120 hours; (b) between 50 and 100 hours.

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