1. You are analyzing a company's stock and bonds traded on public markets. Your analysis produces the following results:

The probability of a significant drop in the stock price given the company has defaulted on its bonds is 0.90;

The probability of a significant drop in the stock price given the company has not defaulted on its bonds is 0.20;

The probability that the company defaults on its bonds is 0.05.

What is the probability that the company has defaulted on its bonds given its stock price had a significant drop?

A. 0.2350

B. 0.1915

C. 0.2368

D. 0.2368

Correct answer is B

A is incorrect. 0.2350 = (0.9*0.05 + 0.2 * 0.95).

B is correct. Let A be the event of default and B be the event of a significant drop in stock price.  By Bayes' Theorem, P(A|B) = P(B|A) * P(A) / (P(B|A) * P(A) + P(B|not A) * P(not A)). So, for the data provided,

P(A|B) = (0.05*0.90)/(0.05*0.90+0.95*0.20) = 0.1915

C is incorrect. 0.2368 = 0.9*0.05 / (0.2 * 0.95).

D is incorrect. 0.0450 = 0.9*0.05.

Reference:  Murray R. Spiegel, John Schiller, and R. Alu Srinivasan, Probability and Statistics, Schaum's Outlines, 2nd ed. (New York: McGraw-Hill, 2000), Chapter 1.

Type of Question: Quantitative Analysis

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