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006Overloaded Server in a Two-Stage Routing SchemeA load balancer routes 4 independent jobs to 3 servers \ S 1, S 2, S 3\ . Server S 1 already holds one pre-assigned job. Each of the 4 new jobs is routed in two stages: first a coin with P( heads ) = \tfrac 1 2 is flipped; if heads the job goes to S 1, if tails the job is sent to S 2 or S 3 each with probability \tfrac 1 2 (i.e., P(S 2) = P(S 3) = \tfrac 1 4 ). A server is called "overloaded" if it holds 4 or more jobs (counting the pre-assigned one for S 1). Construct the sample space for the 4 routing outcomes and compute P( at least one server is overloaded ).概率中等数值题未尝试免费016Distinct Symbols in a Palindromic Access CodeA 5-character access code is formed by choosing each character independently and uniformly from \ A, B, C, D, E, F\ (repetition allowed). The code is then accepted only if it is a palindrome (reads the same forwards and backwards). Among all palindromic codes, find P( at least 3 distinct symbols appear in the code ).概率中等数值题未尝试免费