Financial Risk Manager Part 1

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Explanation:

Explanation

Let's analyze each statement:

Statement A: The probability of a normal market is 0.30

P(Normal market) = P(Good economy) × P(Normal market | Good economy) + P(Poor economy) × P(Normal market | Poor economy)
= (0.60 × 0.30) + (0.40 × 0.30) = 0.18 + 0.12 = 0.30 ✓ ACCURATE

Statement B: The probability of having a good economy and a bear market is 0.12

P(Good economy ∩ Bear market) = P(Good economy) × P(Bear market | Good economy)
= 0.60 × 0.20 = 0.12 ✓ ACCURATE

Statement C: Given that the economy is good, the chance of a poor economy and a bull market is 0.15

This statement is logically inconsistent. If we're given that the economy is good, then the probability of a poor economy is 0 (they are mutually exclusive events).
P(Poor economy ∩ Bull market | Good economy) = 0 ✗ INACCURATE

Statement D: Given that the economy is poor, the combined probability of a normal or a bull market is 0.50

P(Normal or Bull market | Poor economy) = P(Normal market | Poor economy) + P(Bull market | Poor economy)
= 0.30 + 0.20 = 0.50 ✓ ACCURATE

Therefore, statement C is the least likely accurate because it contains a logical contradiction - you cannot have a poor economy given that the economy is good.

Explanation:

Explanation

Let's analyze each statement:

Statement A: The probability of a normal market is 0.30

P(Normal market) = P(Good economy) × P(Normal market | Good economy) + P(Poor economy) × P(Normal market | Poor economy)
= (0.60 × 0.30) + (0.40 × 0.30) = 0.18 + 0.12 = 0.30 ✓ ACCURATE

Statement B: The probability of having a good economy and a bear market is 0.12

P(Good economy ∩ Bear market) = P(Good economy) × P(Bear market | Good economy)
= 0.60 × 0.20 = 0.12 ✓ ACCURATE

Statement C: Given that the economy is good, the chance of a poor economy and a bull market is 0.15

This statement is logically inconsistent. If we're given that the economy is good, then the probability of a poor economy is 0 (they are mutually exclusive events).
P(Poor economy ∩ Bull market | Good economy) = 0 ✗ INACCURATE

Statement D: Given that the economy is poor, the combined probability of a normal or a bull market is 0.50

P(Normal or Bull market | Poor economy) = P(Normal market | Poor economy) + P(Bull market | Poor economy)
= 0.30 + 0.20 = 0.50 ✓ ACCURATE

Therefore, statement C is the least likely accurate because it contains a logical contradiction - you cannot have a poor economy given that the economy is good.

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An analyst develops the following probability distribution about the state of the economy and the market.

| Initial Probability P(A) | Conditional Probability P(B | A) | |--------------------------|----------------------------------| | Good economy 60% | Bull market 50% | | | Normal market 30% | | | Bear market 20% | | Poor economy 40% | Bull market 20% | | | Normal market 30% | | | Bear market 50% |

Which of the following statements about this probability distribution is least likely accurate?

Exam-Like

The probability of a normal market is 0.30.

50.0%

The probability of having a good economy and a bear market is 0.12.

50.0%

Given that the economy is good, the chance of a poor economy and a bull market is 0.15.

Given that the economy is poor, the combined probability of a normal or a bull market is 0.50.