In Code:

`When \\(a \\ne 0\\), there are two solutions to \\(ax^2 + bx + c = 0\\) and they are \\[x = {-b \\pm`

\\sqrt{b^2-4ac} \\over 2a}.\\]

### Quiz Single/Multiple Choice Example (A, BCD)

1. What is the first option?

- Option A
- Option B
- Option C
- Option D

#1 Solution: Option A

2. What are the last three options?

#2 Solution: Options B, C, and D

### AET Test Quiz

1. A group of drivers are classified into equal number of good drivers

and

bad drivers. For a good driver, the probability of getting into one or more auto accident per year is

0.05.

For a bad driver, the probability of getting into N accidents in a year follows a Poisson distribution

with

mean 3.

and

bad drivers. For a good driver, the probability of getting into one or more auto accident per year is

0.05.

For a bad driver, the probability of getting into N accidents in a year follows a Poisson distribution

with

mean 3.

- A. 0.7492
- B. 0.0498
- C. 0.0881
- D. 0.2508
- E. 0.025

#1 Solution: D. 0.2508

This is a Baye’s Theorem question, which will require us to find the following probabilities

This is a Baye’s Theorem question, which will require us to find the following probabilities

- Probability of 1 accident and good driver = X
- Probability of 1 accident and bad driver = Y

And the answer can be derived from \(x \over x + y\)

Since the probability of A and B is the probability of A given B times the probability of B, we have

- \(Pr(one accident | good driver) Pr(good driver)\) = \((0.05)\)(\(1 \over 2\)) = \(0.025\)
- \(Pr(one accident | bad driver) Pr(bad driver)\) = (\(3^1 e^3 \over 1!\))(\(1 \over 2\)) =

\(0.025\)

Finally, the answer is \(0.025 \over 0.025 + 0.074680603\)\(= 0.2505\)