Probability for 3 years and joint probability

[Ceciliya98]

Suppose you are an equity analyst for ABC insurance, you manage a a fund of equity and use historical data to categorise the managers as excellent or average. Excellent managers are expected to out perform the market 70% of the times. Average managers are expected to out perform 50% of the times. Assume that the probabilities of manager is independent of their out perfoming for any given year is independent of their performance in prior years. ABC has found that only 20%. of all fund managers are excellent and remaining 80% are average managers?
ⅰ) A new fund manager and outperformed is the probability to the portfolio started 3 years ago the markels all the three years. What that the new manager was Excellent manager when she first started managing 3 years ago.
ii) Using the above information, find probability that the new manager is excellent or average manager today.
In this i want to know the joint probability for 3 years such that all its sum will be 1. and are we not assuming that a managers can be an excellent and outperform in one year and be average and overperform in second year? and if a managers performance is independent of its previous year performance then how can we know if a manager is excellent or average today based on its performance for last 3 years?

 

[Nicole Seaman]

@Ceciliya98 Can you please provide the source of this question? Do you have a specific question about it? If other members in the forum want to answer, it is helpful for them to know where the question came from and what your specific questions are.

 

[Andrew9654]

To calculate the probability that the new manager was excellent for 3 years, we'll use Bayes' theorem. First, calculate the probability that an excellent manager outperforms the market for 3 consecutive years: (0.7^3). Then, for an average manager: (0.5^3). The sum of these probabilities should equal 1.

No, we are not assuming that a manager can be excellent one year and average the next. Probabilities are independent of prior performance, but the classification of the manager remains consistent.

Greetings, Andrew