ISDS 361B related question on probability

ETF After researching ETF funds, an investor learns that out of 10,000 ETFs, 1,000 outperform S&P500 and 9000 do not. A research analysis has a track record with accuracy of 70% (analysis says buy when ETF outperforms, don’t buy when ETF underperforms). Without having an access to the research analysis, what is the probability that the investor chooses an ETF that outperforms? Without having an access to the research analysis, what is the probability that the investor chooses an ETF that underperfonns? What is the probability that research analysis will recommend an ETF as a buy? What is the probability that research analysis will recommend an ETF as a do-not-buy? What is the probability that an investor invests in an outperform ETF if the research analysis says buy? What is the probability that an investor invests in an undeperform ETF if the research analysis says do not buy? What can you conclude about the value of the research analysis (i.e. how much is it worth compare to just choosing an ETF randomly)?