Consider a computer network system with two identical routers, Router A and Router B$.$ The event $$ denotes the

failure of Router A during the design life, and the event $$ denotes the failure of Router B$.$

In this scenario, the network can still operate if one router fails, but the remaining router is more likely to fail due to

increased usage. If router A fails, the probability of router B failing becomes $20\%.$ If $9\%$ of all network systems

with these routers have at least one router fail by the end of the design life, determine the prior probability of one

router failing, $[$

$],$ during the design life, the probability of both routers failing and the probability that none

of the routers fai