1.What is Pascal's Wager?

A.A bet that one cannot lose
B.An argument for probability theory
C.An argument for the existence of God
D.An argument for why you should believe in God
E.None of the above

2.Who was Pascal?

A.A painter
B.A bishop
C.A mathematician
D.None of the above

3. According to Pascal, what probability should you assign to the existence of God?

A.0
B.1
C.0.5
D.Some number strictly between 0 and 1
E.None of the above

4.According to Pascal, what utility will you get if you believe in God and he exists?

A.0
B.Negative infinity
C.Positive infinity
D.Some finite utility
E.None of the above

5.According to Pascal, infinity multiplied by any finite number is:

A.0
B.A smaller infinity
C.A larger infinity
Undefined
D.None of the above

6.To maximise expected utility is to:

A.Choose the action with maximal possible utility
B.Choose the action with maximal worst-case utility
C.Choose the action that results in the greatest utility, no matter how the world turns out
D.None of the above.

7.The "Many Gods" objection to Pascal's Wager is the objection that:

A.There are many gods, and Pascal assumed otherwise
B.There might be other Gods, and Pascal assumed otherwise
C.Pascal assumed that there are many gods
D.None of the above

8.The pay-offs for the St Petersburg Game are:

A.You get \$$2^N$ if the coin lands “tails” on the first toss
B.You get \$$2^N$ if the coin lands “heads” on the last toss
C.You get \$$1/2^N$ if the coin lands “heads” on the $N$th toss
D.You get \$$1/2^N$ if the coin lands “tails” on the $N$th toss
E.You get \$$2^N$ if the coin lands “heads” on the $N$th toss
F.None of the above

9.The expected utility of the St Petersburg Game:

A.Is infinite, and Pascal used this to argue that you should be believe in God
B.Is a large finite number that we cannot name
C.Is negatively infinite
D.None of the above

10.A mixed strategy is:

A.Any strategy that involves mixing some liquids together
B.Any strategy that leads to a utility mixture of different kinds of infinity
C.Is a strategy of randomly choosing a decision matrix
D.Is a strategy of randomly choosing from a set of basic actions
E.None of the above

11.Pascal's Wager is invalid because:

A.It assumes that anyone should assign some positive probability to God's existence
B.It assumes decision theory
C.It's conclusion is something that no-one should believe
D.It is morally bankrupt
E.There are other choices that minimise expected utility besides believing in God
F.None of the above

And, what are your answers? Or do you want us to do the test for you?

1. The answer is D. Pascal's Wager is an argument for why you should believe in God.

To understand Pascal's Wager, you need to know that Blaise Pascal was a mathematician, physicist, and philosopher in the 17th century. He put forward an argument that deals with the question of whether or not it is rational to believe in God.

2. The answer is C. Pascal was a mathematician.

Now, let's move to the specifics of Pascal's argument.

3. The answer is D. According to Pascal, you should assign some number strictly between 0 and 1 as probability to the existence of God.

Pascal argued that the existence of God is not a matter of certainty, but it is also not a matter of complete uncertainty. Therefore, you should assign some non-zero probability to the existence of God.

4. The answer is C. According to Pascal, if you believe in God and he exists, you will gain infinite utility.

Pascal reasoned that the potential reward for believing in God and living a life devoted to him is eternal happiness in heaven, which he considered to be of infinite utility.

5. The answer is C. According to Pascal, infinity multiplied by any finite number is a larger infinity.

This idea is important in Pascal's argument because the potential utility of infinite happiness in heaven outweighs any finite sacrifices or discomforts in this life.

6. The answer is C. To maximize expected utility is to choose the action that results in the greatest utility, no matter how the world turns out.

Expected utility is a concept in decision theory that involves calculating the probability-weighted average of the utility (or value) of possible outcomes. Pascal argued that believing in God maximizes expected utility because the potential reward of infinite happiness outweighs any potential sacrifices or discomforts.

7. The answer is B. The "Many Gods" objection to Pascal's Wager is the objection that there might be other Gods, and Pascal assumed otherwise.

This objection criticizes Pascal's Wager by suggesting that there might be other gods or deities that exist and reward or punish believers differently. The objection questions Pascal's assumption that the only possible outcome is the Christian God's existence.

8. The answer is F. None of the above.

The pay-offs for the St Petersburg Game are not listed among the given options. It is important to note that the St Petersburg Game is a separate concept and not directly related to Pascal's Wager.

9. The answer is A. The expected utility of the St Petersburg Game is infinite, and Pascal used this to argue that you should believe in God.

The St Petersburg Game is a thought experiment that involves a series of coin tosses and escalating payouts. The expected utility of the game, calculated using probability theory, turns out to be infinite. Pascal used this idea to illustrate that even though the individual payouts may start small, the potential for infinite reward justifies believing in God.

10. The answer is D. A mixed strategy is a strategy of randomly choosing from a set of basic actions.

In game theory, a mixed strategy refers to a player's strategy in which they randomly select from a set of available actions with specific probabilities. This randomization is often used to maximize a player's expected payoffs.

11. The answer is E. There are other choices that minimize expected utility besides believing in God.

One of the criticisms of Pascal's Wager is that it assumes that the only choices are to believe in God or not believe in God. However, there are alternative belief systems or positions that could also be considered in terms of maximizing expected utility. Therefore, Pascal's Wager may not be the only valid argument in decision-making.