Compound Random experiment: Flip a penny, draw a marble from a bag containg 3 red, 5 orange, and 2 green marbles. Draw the tree diagram to represent this compound random experiment. List the sample space. Compute the probabilities for each of the atomic events of the sample space. Event A = { Red marble and head on penny or green marble tail on penny} Event B = { orange or green marble and head or tail on the penny} Calculate: p(A), p(b), p(A union B), and finally determine if they are independent events. Remember to defend your answer as answers

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Q: If an unbiased dice is rolled once, the odds in favour of getting a point which is multiple of 3 is:

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Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.