4) Fund managers fall into one of three categories:

• Stars, who outperform the market 60% of the time
• Average who outperform the market 40% of the time (50% of all fund
• managers are average).
• Poor who outperform the market 30% of the time
• Performance in each period is independent of performance in prior periods.
• A manager, Sansa, has outperformed the market three periods in a row. You have just been told that based on this performance, and given the proportion of fund managers who are stars, that the probability that Sansa is a star fund manager is 25%.

What proportion of fund managers are stars?