3. Two players, High and Low, play the following game on the "board" shown below. They place a coin on the top node, and then they take turns to move the coin one node downward until the coin arrives at one of the sixteen terminal nodes. High's goal is that the game ends with the coin at a node with as high a value as possible, while Low's aim is that the target node has as low a value as possible. Assuming that both of them play optimally, what is the outcome (the value of the last node) of the game if: (a) High starts? (b) Low starts? A 1 14 7 12 3 16 6 10 2 13 4 11 5 15 8 9

Students in a class like to secretly use online calculators in their quizzes. There are three such online calculators favoured amongst the students: WolframAlpha (WA), Symbolab (S), and GeoGebra (GG). A student's favourite calculator changes from quiz to quiz according to the following rules: If a student likes WA best, then it is has a 50% chance of remaining their favourite for the next quiz; 25% of becoming S for the next quiz; and 25% of becoming GG for the next quiz.  If a student likes S best, then it has a 50% chance of becoming WA for the next quiz, and a 50% chance of becoming GG for the next quiz.  If a student likes GG best, then it has a 33.3% chance of becoming any of the three calculators for the next quiz.  For the first quiz, there are 120 who count WA as their favourite; 80 who count S as their favourite; and 50 who count GG as their favourite.  What is true about the fourth quiz? Choose one of the following: 1. 115 students favour WA; 52 students favour S; and 83…

Suppose that after the 2020 presidential election there are three races that are too close to call: Wisconsin,Michigan, and Pennsylvania. In order to become president, a candidate must receive 270 electoral votes ormore. Wisconsin has 10 electoral votes, Michigan has 16, and Pennsylvania has 20. Suppose that in theother decided races, Democrats have 259 electoral votes and Republicans have 233. The Democrat has an80% chance of winning Wisconsin, a 50% chance of winning Michigan, and a 10% chance of winningPennsylvania. A statistician defines a random variableXto be +1 if the Democrat wins,−1 if theRepublican wins, and 0 if neither candidate reaches 270 electoral votes. Find the probability densityfunction ofX. (Hint: Make this easier by figuring out the scenario in which the Republican wins or there isa tie!)

Valve A: 92% Valve B: 94% Valve C: 93%

A car wash has three different types of washes: basic, classic, and ultimate. Based on records, 45% of customers get the basic wash, 35% get the classic wash, and 20% get the ultimate wash. Some customers also vacuum out their cars after the wash. The car wash records show that 10% of customers who get the basic wash, 25% of customers who get the classic wash, and 60% of customers who get the ultimate wash also vacuum their cars. The probabilities are displayed in the tree diagram.What is the probability that a randomly selected customer purchases the basic or classic car wash if they vacuum their car?A) 0.13B) 0.48C) 0.52D) 0.80

2.

A researcher is interested in the effects of cocaine on learning. A group of rats is randomly assigned to receive either cocaine or a non-harmful saline solution. The rats are taught how to run a maze. The cocaine rats need to be reared away from the control group rats, so they are handled and taught by one experimenter, and the control group rats are handled and taught by another experimenter. The results showed that the control group rats learned how to run the maze more quickly than the cocaine rats. 1. What is the independent variable? 2. What is the dependent variable? 3. What is the confounding? 4. How could the confounding be fixed?

Read the paper above and answer question # 4 only