The Ontario Lottery Group has recently started allowing betting on the outcomes of games of the Canadian Calvinball League. It costs $10 to purchase a ticket, and you must successfully determine the outcome of the night's games. Tonight the games are Oakville Owlbears Brampton Beholders Whitby Wyverns vs Vs Vs Mississauga Mind Flayers Guelph Githyanki Kitchener Kuo-Toa You will win 3k - 1 dollars for correctly determining the outcome of k matches. Question 1 Assuming all teams are equally matched, what are your expected net winnings? Note that your net winnings are the difference between what you paid to play and what you won. Hence your winnings can be negative if you lose money. Question 2 Per the rules of Calvinball, the team whose name occurs first alphabetically has an advantage and is twice as likely to win their game. Assuming you bet on the more likely winner in each game, what are your expected value net winnings? Question 3 You have a friend who plays for the Whitby Wyverns. The team found a ringer from the European leagues, and the likelihood that the Wyverns win their next game is now 100%. Assuming that you bet for the Wyverns and that the other two games still favour the alphabetical team, what are your erpected net winnings?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
question 3
![The Ontario Lottery Group has recently started allowing betting on the outcomes of games of the Canadian
Calvinball League. It costs $10 to purchase a ticket, and you must successfully determine the outcome of the night's
games. Tonight the games are
Oakville Owlbears
Brampton Beholders
Whitby Wyverns
VS
Vs
Vs
Mississauga Mind Flayers
Guelph Githyanki
Kitchener Kuo-Toa
You will win 3* – 1 dollars for correctly determining the outcome of k matches.
Question 1 Assuming all teams are equally matched, what are your expected net winnings? Note that your net
winnings are the difference between what you paid to play and what you won. Hence your winnings can be negative
if you lose money.
Question 2 Per the rules of Calvinball, the team whose name occurs first alphabetically has an advantage and is
twice as likely to win their game. Assuming you bet on the more likely winner in each game, what are your expected
value net winnings?
Question 3 You have a friend who plays for the Whitby Wyverns. The team found a ringer from the European
leagues, and the likelihood that the Wyverns win their next game is now 100%. Assuming that you bet for the
Wyverns and that the other two games still favour the alphabetical team, what are your expected net winnings?
1. Suppose f is a function which satisfies f(x + y)
Numeracy 1
value of f(0)?
f(x) + f(y) for all , y E R. What is the
%3D
2. Let f(x) = e + r3 + x-3. This function is invertible. What is the value of f-1(-2)?
3. Consider the function f, defined on R, whose graph on the interval [-3, 3] is given below:
-2
-1
1
2
Assuming that the function maintains this pattern of behaviour on all of R, give an algebraic description of the
function f; that is, write down f(x) in such a way that we can compute the value of f for any given x E R.
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