Question

An engineering system consisting of n components is said to be a $k$-out-of-$n$system $(k\dots n)$if the system functions if and only if at least $k$of the $n$components function. Suppose that all components function independently of one another.

(a) If the ith component functions with probability$Pi,i=1,2,3,4$, compute the probability that a $2$-out-of-$4$system functions.

(b) Repeat part (a) for a $3$-out-of-$5$
system

Short answer

a). nkvdnvkiadndsivn

Step-by-step solution

Given Infromation (Part a)

Let's name the events

$S=\left\{\text{the}2\text{-out-of-}4\text{system functions}\right\}$

$A_i=\left\{\text{the}i\text{-th component functions}\right\},i=1,2,3,4$

Explanation (Part a)

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