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 \(0.025 \over 0.025 + 0.074680603\)\(= 0.2505\)
