k-out-of-n Systems. Suppose that n independent components constitute an engineering system. The system is called a k-out-of-n system if it works only when k or more components are operational. This...

k-out-of-n Systems. Suppose that n independent components constitute an engineering system. The system is called a k-out-of-n system if it works only when k or more components are operational. This particular system has four components that are operational with probabilities 0.1,0.8,0.5, and 0.4. If the system is a 2-out-of-4, what is the probability that it works?

Number of Dominos. How many different dominos are a sample space if the number of dots on the dominos ranges between (a) 0 and 3, (b) 0 and 8, and (c) 0 and 16, inclusive?