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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- Option : B
- Explanation : A probability of an event given (conditioned on) another event is a conditional probability.

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- 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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