3.67 - A First Course in Probability

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

Step-by-Step Solution

Answer

a). nkvdnvkiadndsivn

Step 1: Given Infromation (Part a)

Let's name the events

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

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

Step 2: Explanation (Part a)

nknknknmmmmmmmmccmxcmzxczxczx