Probablity Concepts

11 questions

1. 1. Suppose that the probability of event A is 0.2 and the probability of event B is 0.4. Also, suppose that the two events are independent. Then P(A|B) is:
   P(A) = 0.2 P(A)/P(B) = 0.2/0.4 = ½ P(A) × P(B) = (0.2)(0.4) = 0.08
2. 2. An event has a 0.25 probability of occuring. What are the odds against the event occuring?
   One-to-fourOne-to-threeThree-to-one
3. 3. The Addition Rule to determine the probability of either event A or event B occurring is stated as P(A or B) = P(A) + P(B) – P(A and B). Why is P(A and B) subtracted?
   This rule determines the probability of event A or B occurring, not A and B, so this factor is subtracted.You do not have to subtract P(A and B) if A and B are statistically independent.P(A and B) has been counted twice through P(A) and P(B).
4. 4. An investment advisor currently maintains a list of 15 recommended stocks. If a particular client would like to invest in 5 stocks, how many possible portfolios exist?
   753,003360,360
5. 5. A large investment banking firm is announcing the awards for the top portfolio managers. They have total 8 portfolio managers and the top three analysts will receive first, second and third-place awards. Calculate the total number of ways in which the three awards can be given.
   656336
6. 6. A research analyst has established the prior probabilities for a company's next year's revenue exceeding, remaining same, or being below the previous year's revenue.

   Revenue will exceed previous year's revenue = 30%.

   Revenue will be the same as previous year's revenue = 50%.

   Revenue will be below previous year's revenue = 20%.

   After some time there is news about the company firing 10% of its staff. With this new information, the analyst revises his information and estimates the likelihood that the company will fire employees given that the revenue exceeds, remains same, or is below previous year's revenue.

   P(Firing employees | Revenue exceeds) = 10%

   P(Firing employees | Revenue same) = 20%

   P(Firing employees | Revenue less) = 70%

   Using the Bayes' formula, calculate the updated probability that the company's revenue will be less than previous year's revenue.

   0.200.270.52
7. 7. In a lucky draw, 200 names are put in a box. 5 of these names are same. You are asked to take one name out of the box. What is the probability that this name is of the five similar names.
   0.0050.0250.125
8. 8. An investor invests in 20 different stocks. Out of these 20 stocks he has selected 16 after conducting thorough research and the rest four were selected based on the recommendation by his broker. If you select one random stock, what is the probability that this stock was recommended by his broker?
   0.050.200.80
9. 9. You have a portfolio of 100 stocks. Out of these 100 stocks 30% stocks had outstanding performance and 70% stocks had fair performance. 60% of these stocks are of manufacturing companies.

   If you select a stock randomly, what is the probability that it is either an outstanding performance stock or it is a manufacturing company stock.

   0.180.720.90
10. 10. The probability that GDP will rise is 0.70. The probability that a company’s stock price will rise given a rise in GDP is 0.60. The probability that the company’s stock price will rise given no rise in inflation = 0.40.

    Calculate the probability that the stock price will rise.

    0.240.541
11. 11. The probability that GDP will rise is 0.70. The probability that a company's stock price will rise given a rise in GDP is 0.60. The probability that the company's stock price will rise given no rise in inflation = 0.40.

    Calculate the probability that both GDP and stock price will rise.

    0.240.540.42