A few years ago, The United States was developing a national missile defense system.$$ The system would have been able to fire $4$ interceptors at each incoming warhead.$$ Each interceptor would have a $75\%$ chance of destroying an incoming warhead.$($This question might prove useful if North Korea ever starts sending out missiles directed towards the United States$).$

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a$).$ If the performance of each of the $4$ interceptors is independent of the others, what is the probability that an incoming warhead would survive and penetrate the defense?