In the game Mastermind, one player guesses a four-color code (represented by pegs). There are 9 colors to choose from. The order of the colors matters, and let's say the code has four unique colors. Define the events Y, B, and R as follows: Y: The third peg is yellow. B: The first peg or the third peg is blue. R: The code contains a red peg and white peg consecutively (in that order). a Calculate the probability of each event: p(B), p(R), and p(Y) b What is p(BY)? c What is p(BIR)? d What is p(R/Y)? e Consider all pairs of events: (B,Y). (B, R), and (R,Y). Which pairs are events are independent and which pairs are not independent? Justify your answers using one of the independence tests we learned.

Nim is a two-player game played with several piles of stones. You can use as many piles and as many stones in each pile as you want, but in order to better understand the game, we'll start off with just a few small piles of stones (see figure 1 below). Pile 1 Pile 1 Pile 2 The two players take turns removing stones from the game. On each turn, the player removing stones can only take stones from one pile, but they can remove as many stones from that pile as they want (please note, a player must remove atleast 1 stone from a pile during his/her turn). If they want, they can even remove the entire pile from the game! The winner is the player who removes the final stone (avoid taking the last stone - see figure 2 below). Pile 2 Pile 3 Pile 3 Let's say its Max (player 1) turn to play. Then Max can win by simply removing a stone from Pile 2 or Pile 3 Draw a game tree (upto depth level 2) for the given version of the Nim game. Please consider figure 1 as your initial game configuration/state…

Python tic tac toe. Tic tac toe is a very popular game.  Only two players can play at a time.  Game Rules Traditionally the first player plays with "X". So you can decide who wants to go with "X" and who wants to go with "O". Only one player can play at a time. If any of the players have filled a square then the other player and the same player cannot override that square. There are only two conditions that may match will be a draw or may win. The player that succeeds in placing three respective marks (X or O) in a horizontal, vertical, or diagonal row wins the game. Winning condition Whoever places three respective marks (X or O) horizontally, vertically, or diagonally will be the winner. Submit your code and screenshots of your code in action.  Hints : Have a function that draws the board  Have a function that checks position if empty or not Have a function that checks player or won or not    expected output:

Python tic tac toe. Tic tac toe is a very popular game.  Only two players can play at a time.  Game Rules Traditionally the first player plays with "X". So you can decide who wants to go with "X" and who wants to go with "O". Only one player can play at a time. If any of the players have filled a square then the other player and the same player cannot override that square. There are only two conditions that may match will be a draw or may win. The player that succeeds in placing three respective marks (X or O) in a horizontal, vertical, or diagonal row wins the game. Winning condition Whoever places three respective marks (X or O) horizontally, vertically, or diagonally will be the winner. Submit your code and screenshots of your code in action.  Hints : Have a function that draws the board  Have a function that checks position if empty or not Have a function that checks player or won or not    expected output: