According to data from the ABS, the total asset under management $($AUM$)$ in the managed funds market is around $1\mathrm{.}7$ trillion dollars, with $1\mathrm{.}475$ trillion dollars in active management and about $225$ billion dollars in passive funds. Despite the growing interest in passive funds, active management still dominate the industry. Mary is deciding whether to allocate her funds into active or passive investments.

$($a$)$ Outline the differences between active and passive investment strategies. What assumptions about market efficiency underpin each investment approach?