# Computing the Probability of Choice

A color candy was chosen randomly out of a bag. Below are the results:

Color Probability

Blue 0.30

Red 0.10

Green 0.15

Yellow 0.20

Orange ???

a. What is the probability of choosing a yellow candy?

b. What is the probability that the candy is blue, red, or green?

c. What is the probability of choosing an orange candy?

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A. from the question, the probability of choosing a yellow candy is ...

#### Solution Summary

The solution gives detailed steps on computing the probability in of choosing an instance.

Your role is to compute the expected value for the "Reject Christ" decision and pick the "best" choice to make.

The expected value concept is important and used in Decision Analysis. Decision Analysis can help make decisions based on the probability of different sates of nature from occurring, with different events from each decision being assigned a monetary value. The analysis computes the expected value of each decision, and identifies the decision having the largest expected value (which you would typically choose).

The simple example described herein is adapted from Pascal's Wager, named after Blaise Pascal (1632 - 1662), a brilliant French mathematician Let's assume the following two states of nature: that either God exists, or He doesn't. There are no other states possible. Then, let's say there is only a 10% probability that God exists, and a 90% probability that God does not exist (i.e., there is no God). Notice that the probabilities must sum to 100%.

Next, you have a decision with two options: either to accept Christ or reject Christ. If you accept that Christ and God exist, the result is that you go to heaven, which we will assign a monetary value of $100. If you accept Christ and there is no God, you will have lived a good, clean life with no afterlife, which we assign an assumed monetary value of $10. If you reject Christ and God exists, you will spend eternity in hell, which is just as bad as heaven is good, so we assign a monetary value of -$100. If you reject Christ and there is no God, then you have lived a normal life with no afterlife, which we assign a monetary value of $5. You can see we have made the brash assumption that, on the average, a "good, clean" Christian life would be expected to be void of drunkenness, smoking, drugs, fornication, and other behaviors admonished in the Bible, so would have a slightly higher monetary value than a life that includes these activities.

Finally, we compute the expected values. If you accept Christ, you have a 10% probability of earning $100 if God exists, and a 90% probability of earning $10 if there is no God, which gives an expected value of:

(0.10)($100) + (0.90)($10) = $19.00

The table illustrating this analysis is provided here.

Table for Decision Analysis (SEE ATTACHED)

Your role is to compute the expected value for the "Reject Christ" decision and pick the "best" choice to make.

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