let drawing a red and green marble are represented by R and G
P(player 1 wins) =P(R)+P(GGR)+P(GGGGR)
=(2/7)+(5/7)*(4/6)*(2/5)+(5/7)*(4/6)*(3/5)*(2/4)*(2/3)=4/7
10. (16 points) A jar contains 2 Red marbles and 5 Green marbles. Players 1 and 2 take turns withdrawing marbles from the jar (without replacing them). Whoever selects a Red marble first wins the gam...
Suppose an opaque jar contains 7 red marbles and 10 green marbles. The following exercise refers to the experiment of picking two marbles from the jar without replacing the first one. What is the probability of getting a green marble first and a red marble second? (Enter your probability as a fraction.) this problem is posted on your page, however, the answer is incorrect. Thank you!
4. A jar contains 6 red, 5 green, 4 blue, and 2 yellow marbles. Four marbles are selected without replacement. Determine the probability of the following: DO NOT REDUCE a) One marble of each color is selected. b) The first three marbles are blue and the last marble is yellow. c) All the marbles are blue d) The first two marbles are red and the last two marbles are purple. 5. HORIZON, a national TV provider, reports that today's typical...
Exercise 1. Two players, 1 and 2, take turns choosing numbers; 1 goes first. On his turn, a player may choose any number between 1 and 10, inclusive, and this number is added to a running total. When the running total of both players’ choices reaches 100, the game ends. The player whose choice of number takes the total to exactly 100 is the winner. (i) Who wins the game when we solve it using backwards induction? (ii) Provide a...
1. NIM game. This is a different version or easier version of NIM game Consider a pile of 5 matchsticks. Two people take turns removing 1 or 2 sticks each time from this pile. Suppose both players play smartly (nobody plays a fool move trying to let the opponent wins. But there is only one winner anyway) a)If the person getting the last stick wins, will the first player win? Why? Show the steps the first and second player will...