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3. A computer system uses passwords that contain exactly eight characters, and each character is one of the 26 lowercase letter (a -z) or 26 uppercase letters (A - Z) or 10 integers (0-9). Let Ω denote the set of all possible passwords. Suppose that all passwords in Ω are equally likely. Determine the probability for each of the following: (a) Password contains all lowercase letters given that it contains only letters (b) Password contains at least 1 uppercase letter given that it contains only letters (c) Password contains only even numbers given that it contains all numbers

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Total number o baractes Cb) 26C uppercase letters tal Do of Pass coords which coniai 2 wor 2 6 Least l apperaue lesters which IO Ce- diglt s cont th letters 6 2 ith all ouber Case le posfos the pass od of 8 digit irst digit car be chesen in 62 w4s (26 (62)3a6ア 5 2 Requirea probabill 5 2 oss ble Pass osds (s 2) 8 2 se letters 2SG There are 26 oercase letter」-, so urn ber of passib) Total no o Pass word.s th d contain D lejters (6 2) 8 0-92 26)8 ! i Required pmobab C(a) & 2S6 2S 6

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