Problem 1. You are playing a version of the roulette game, where the pockets are from 0 to 10and even numbers are red and odd numbers are black (0 is green). You spin 3 times and add up the values you see. What is the probability th at you get a total of 17 given on the first spin you spin a 2? What about a 3? Solve by simulation and analytically.

We have n glasses which can hold a varying amount of liquid. We will say that glass1 is size q1 quarts and glass2 is size q2 quarts, etc. We now give you a size, say x quarts. You must give me a glass of exactly x quarts.  You are allowed to fill any glass to exactly its size and to pour any liquid from one glass into another.  When you pour, you either have to empty the glass you are pouring from or fill the glass you are pouring into.  Can you do it?More concrete example: G1 has size 10 quarts.  G2 has size 4 quarts.  G3 has size 1 quart.  You can get a 5 quart drink by filling G1, pouring 4 quarts from it into G2 and 1 quart of it into G1.  After that, G1 has exactly 5 quarts. In the same problem, we could get 8 quarts by filling G2 twice and emptying it into G1 twice.   Given This: Write an algorithm to do this and determine its complexity.

In the game of 10-pin bowling the bowler has two attempts to knock down pins for every frame of 10-pins, and scores a point for each pin knocked down. If all the pins are knocked down with two attempts, the bowler gets a bonus - whatever score they obtain with their next bowl is doubled. If all the pins are knocked down on the 1st attempt, no 2nd attempt is allowed, and the bowler gets a bonus – whatever score they obtain on their next two bowls are doubled. A student attempts to capture this scoring system in VHDL code, a fragment of which is shown in Figure Q4. Q4 (a) Draw the state transition diagram described by the VHDL of Figure Q4. Discuss whether the VHDL of Figure Q4 correctly scores a game of 10-pin bowling. (b) elsif CLK='1' and CLK'event and UPD='1' then case present state is when throwl => frame := frame + 1; + resize (unsigned (N), 9) score := score if N = w1010" then present state score := score + resize (unsigned (N), 9) present state + resize (unsigned (N),9) if N =…

Imagine there are N teams competing in a tournament, and that each team plays each of the other teams once. If a tournament were to take place, it should be demonstrated (using an example) that every team would lose to at least one other team in the tournament.

6. AND Since there are two zeros on the board, let's determine the probability that you would be able to cover them on 2 consecutive turns. This means you'd have to roll a zero and then roll another zero. You can think of this as an AND probability. You need to roll 0 AND then you need to roll 0 again. Since the result of the first roll will have no influence on the result of the second roll, you can use the following rule: P(A and B) = P(A) * P(B) a) Determine P(0 and 0). b) Determine 1 - P(0 and 0). c) Write a sentence describing the meaning of 1 - P( Oand 0 ).