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The probability of page fault happening is $\frac{1}{k}$.

Hence, the probability of page fault not happening is $1-\frac{1}{k.}$

Therefore, total time is given as:

$(1-\frac{1}{k})t + \frac{1}{k}t_1$ which comes out to $t + \frac{t_1 - t}{k}$
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