Quantitative Methods - Quantitative Methods Section 2

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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.
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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%

  • 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.
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23. The odds for a company’s share price to fall below $45 are 1 to 5. The probability of the event occurring is closest to:

  • 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.
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25. Consider two independent events, A and B, with unequal probabilities (i.e. P(A) ≠ P(B)), then the probability of event A given that event B has occurred (i.e., P(A│B)) is best described as:

  • 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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