Empirical, Subjective and Priori Probability

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5 questions

1. 1. A portfolio manager estimates a 30% chance of a Federal Reserve rate hike next month, based on her interpretation of recent economic indicators and professional experience. This is an example of which type of probability?
   Empirical probabilityA priori probabilitySubjective probabilityConditional probability
2. 2. Which of the following best distinguishes a priori probability from empirical probability?
   A priori probability requires large historical datasets; empirical probability does not.A priori probability is derived through deductive reasoning from prior knowledge, while empirical probability is derived from observed data.A priori probability is always more accurate than empirical probability.Empirical probability involves logical deduction; a priori probability involves data collection.
3. 3. A risk analyst reviews 500 historical trading days and finds that a stock fell on 150 of those days. She estimates the probability of a down day as $\frac{150}{500} = 0.30$. Which probability type is this?
   Subjective probabilityA priori probabilityEmpirical probabilityUnconditional probability
4. 4. Which of the following scenarios represents an a priori probability?
   An investor believes there is a 60% chance a merger will succeed based on her industry contacts.A credit analyst calculates a 4% default rate based on 10 years of loan data.The probability of drawing an Ace from a standard 52-card deck is determined to be $\frac{4}{52}$.A trader assigns a 25% probability to a market crash based on gut feeling.
5. 5. An analyst can use more than one type of probability in practice. Which of the following statements is most accurate?
   Subjective and empirical probabilities always produce the same estimate for the same event.When historical data is unavailable or insufficient, subjective probability may be the only practical option.A priori probability is the preferred method in finance because financial markets follow strict logical rules.Empirical probability is unsuitable for financial applications.