Quantitative Methods - Quantitative Methods Section 2
21. Which of the following types of probabilities is most likely based on logical analysis?
- Option : B
- Explanation : A priori probability is based on logical analysis, an empirical probability on historical data, and a subjective probability on personal or subjective judgment.
22. The probabilities of earning returns are as follows:
| Probability | Return |
| 0.20 | 15% |
| 0.20 | 20% |
| 0.20 | 7% |
| 0.20 | 12% |
| 0.20 | 13% |
What are the odds of earning at least 15%?
- Option : A
- Explanation : The odds of an event can be determined by dividing the probability of the event occurring by the probability of the event not occurring. As a formula this can be expressed as: P(E) / (1 – P(E)). In this case the probability of the event (earning at least 15%) is 0.20 + 0.20 which 0.40. The probability of the event not occurring (earning less than 15%) is 0.20 + 0.20 + 0.20 = 0.60. Hence the odds are 0.40/0.60 = 2/3. This can also be written as 2 to 3.
- Option : A
- Explanation : The probability of an event occurring given the odds for it is calculated as follows: Probability of E given odds of a to b = a / (a+b) = 1 / (1+5) ≈ 0.17.
- Option : B
- Explanation : A probability of an event given (conditioned on) another event is a conditional probability.
- Option : A
- Explanation : Two events, A and B, are independent if and only if P(A│B) = P(A) or, equivalently, P(B│A) = P(B). The wording of the question precludes P(A) = P(B); therefore, responses B and C cannot be correct.
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