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1. A unique ID number is given to each employee at a company. The ID number starts with a vowel followed by an odd digit. (a) Sketch the tree diagram for this experiment (b) list the elements in the sample space (e) define the event "A" which is the set of IDs with a digit greater than 5 (d) define the event "B" which is the set of IDs with a vowel before the letter "j" (e) define the event "C" which is the set of IDs with a vowel after the letter "g" (f) determine the number of elements in the following events i. (ANB) UC" ii. B'nc" iii. (A'U B') iv. (A'U B)n (BUC) 2. Consider the following experiment where you are going to toss a coin, if you get a head you roll a die, while if you get a tail you toss a coin again. You stop the experiment only if you either toss two tails in a row or roll a die. (a) Sketch the tree diagram for this experiment (b) define the event "A" which is rolling an odd number (e) define the event "B" which is tossing at most one head (d) define the event "C" which is tossing at least one tail (e) Are the following events mutually exclusive? Justify. i. A and B ii. B and C 3. How many distinct permutations can be made from the letters of (a) your first name (b) your last name (c) the word "computer" (d) the word "electrical 4. From a deck of cards, you are going to select five cards at random without replacement. How many ways can you select five cards that contain (a) two queens (b) four spades and one heart (e) four red cards (d) five kings 5. Consider an experiment whose sample space is the set S= {x|x 2.0 < I