A system is composed of five components, each of which is either working or failed. Consider an experiment that consists of observing the status of each component, and let the outcome of the experiment be given by the vector (x1, X2, X3, X4, X5), where x¡ is equal to 1 if component i is working and is equal to 0 if component i is failed. a) How many outcomes are in the sample space of this experiment? b) Suppose that the system will work if components 1 and 2 are both working, or if components 3 and 5 are both working. Let w be the event that the system will work. Specify all the outcomes in W. c) Let A be the event that components 2 is failed. How many outcomes are contained in the event A? d) Write out all the outcomes in the event A°n W.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
c and d parts
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