Hey everyone - This is my first time posting. Taking the exam in June, here in about a month. I’ve been trying to work on this Bayes Formula problem all day… Adolphus Sisti, CFA, is an equity analyst with an investment banking firm. Sisti’s area of expertise is Initial Public Offerings (IPOs). He wants to determine whether he can improve his chances of investing in firms that will be successful. In the particular industry that he tracks, it appears that acceptance by a venture capital firm greatly improves the odds of success. Currently, he is following 50 start-ups who have either been accepted or rejected by venture capital firms. A research analyst in the firm provides the following information: · The probability that a start-up company in the sample will fail is 80%. · 25% of firms accepted by venture capital firms will fail after they receive financing. · 75% of firms accepted by venture capital firms will succeed after they receive financing. Assuming that Sisti randomly selects a start-up company from the sample, which of the following statements is TRUE? A) If Sisti randomly selects a start-up that has been accepted by a venture capital firm, the probability that the firm will fail is approximately 0.46. B) The probability that a start-up will fail plus the probability that the start-up will succeed is less than 1. C) Sisti’s chance of randomly selecting a start-up that a venture capital firm has accepted is 0.55. D) The information that the stock he randomly selects has been accepted by a venture capital firm does not improve his chances of investing in start-ups likely to succeed. I pulled this problem from an old Schweser practice text. I know that answer B can be ruled out immediately per probability definition. According to the answers at the back of this test the answer is A. I have the Bayes Formula memorized but sometimes have a hard time pulling some of the info required out from the problem. In this case, I’m having trouble interpreting the bottom two bullet points above. Also, the answer explanation given at the end of the particular test leaves a little to be desired for this problem. Can someone work through this problem real quick to confirm the information in answer A and post their steps? Thanks
Ouch… without knowing the probability of being accepted by a VC, it does not look like it is solvable! INMHO.
They messed up (surprise - Schweser messed up a prob problem). That 75% is probably supposed to be P(Fail | not accepted by VC) and then you have a standard Bayes question.
This is the explanation that was given at the bottom of the test with all the answers… I tried to follow along and make sense of the problem, but to no avail. To calculate this probability, we will use Bayes’ theorem: First, we will calculate the probability that that a start-up is accepted by a venture capital firm, since this is the denominator of Bayes’ Theorem. = [P(Accepted & Fail) * P(fail)] + [P(Accepted & Succeed) * P(succeed)] = [(0.25 *0.8) + (0.75 * 0.2)] = 0.35 Note: This also shows that the choice, “Sisti’s chance of randomly selecting a start-up that a venture capital firm has accepted is 0.55” is false. Then, The P(Accepted & Fail) = (0.2 / 0.35) * 0.8 = 0.46 Explanation for other false choices: • Using the same denominator calculated above and Bayes’ Theorem to calculate a posterior probability: The P(Accepted & Succeed) = (0.75 / .35) * 0.2 = 0.43. Once Sisti knows that a start-up has been accepted by a venture capital firm, the probability that that start-up will succeed increases from 0.20 (given) to 0.43. Thus, the information increases his chance of investing in start-ups likely to succeed. • By definition, the probability that a start-up will fail plus the probability that the start-up will succeed is equal to 1.
when reading the options: B is obviously wrong. Same for D (in the question, “it appears that acceptance by a venture capital firm greatly improves the odds of success”) So basically you have to select between A and B. They both have in common the fact that the analyst selected a company that has been accepted by the Venture Capital firm. Which means, we need to get the probability of such an event happening. P firm fail = 0.8 P firm succeed = 0.2 P firm selected fail = 0.25 P firm selected succed = 0.75 P firm seleced = 0.2 * 0.25 + 0.2*0.75 = 0.35 That tells us that C is wrong, which means that A is right.
This confuses me about this question: If Sisti randomly selects a start-up that has been accepted by a venture capital firm, the probability that the firm will fail is approximately 0.46. Isn’t this just P(Fail | Accepted)? The question is worded as, Sisti has picked an accepted firm, what is the probability of failure? Not if he randomly picks a firm, what is the joint prob of accept and fail?
asayers Wrote: ------------------------------------------------------- > This is the explanation that was given at the > bottom of the test with all the answers… I > tried to follow along and make sense of the > problem, but to no avail. > > To calculate this probability, we will use Bayes’ > theorem: > > First, we will calculate the probability that that > a start-up is accepted by a venture capital firm, > since this is the denominator of Bayes’ Theorem. > > = + > > = [(0.25 *0.8) + (0.75 * 0.2)] = 0.35 > > Note: This also shows that the choice, “Sisti’s > chance of randomly selecting a start-up that a > venture capital firm has accepted is 0.55” is > false. > > Then, The P(Accepted & Fail) = (0.2 / 0.35) * 0.8 > = 0.46 > > Explanation for other false choices: > > • Using the same denominator calculated above and > Bayes’ Theorem to calculate a posterior > probability: The P(Accepted & Succeed) = (0.75 / > .35) * 0.2 = 0.43. Once Sisti knows that a > start-up has been accepted by a venture capital > firm, the probability that that start-up will > succeed increases from 0.20 (given) to 0.43. Thus, > the information increases his chance of investing > in start-ups likely to succeed. > > • By definition, the probability that a start-up > will fail plus the probability that the start-up > will succeed is equal to 1. This is just incorrect. Ignore it.