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.
• 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

• 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$