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Andrew S. Tanenbaum (OS) Edition 4 Exercise 5 Question 21 (Page No. 431)

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Answer:

The probability of $0$ failures, $\mathbf {P_0}: $$(1-\mathrm p)^{\mathrm k}$

The probability of $1$ failures, $\mathbf {P_1}: $$\mathrm{kp}(1-\mathrm p)^{\mathrm k-1}$

$\therefore$ Probability of a $\mathbf{RAID}$ failure $=1-\mathrm {P_0}-\mathrm{P_1} = 1-(1-\mathrm p)^{\mathrm k}-\mathrm{kp}(1-\mathrm p)^{\mathrm k-1}$

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