The Fund That Never Lost
1 in 100 fund managers is genuinely skilled, and a skilled manager beats the market in any given year with probability $3/4$ (independently across years). The other 99 in 100 have no skill and beat the market with probability $1/2$ each year, independently. You select, from the whole population, a manager who has beaten the market in each of the last 5 years. What is the probability she is skilled? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- The Two Coins 4.0/10
Source: Base-rate reasoning for streak-selected fund managers; a standard Bayes exercise. Statement written for AxiomIQ.