There are about $7500$ actively managed mutual funds and ETFs in the US$.$ Assume each one has a $50\%$ chance of "beating the market" $($i$.$e$.,$ the deviation from "average" market performance is due to pure luck and no skill$),$ how many of them would you expect to consistently beat the market every single year over a $7-$year period? How many would outperform more often than underperform $($i$.$e$.,$ outperform in four or more years$)?$ A cursory search turned up a number, $2\mathrm{.}4\%,$ to be the fraction of funds that have cutperformed S