Larry is a high school senior. Larry$$s goal in life is to either $(1)$ become a partner at the most

elite business law firm in the world or $(2)$ become a professional football player in the National

Football League.

The law firm, Dewey, Cheathum, & Howe, only hires their associates from Harvard Law School.

To make partner at DCH$,$ the employee must remain employed at the firm for six $(6)$ years. The

average length of employment for a new hire at the law firm is $4\mathrm{.}5$ years, and the distribution

for employment actually follows an exponential distribution.

To get accepted into Harvard Law School, a student must score a minimum of a $167$ on the LSAT

and have a $3\mathrm{.}85$ GPA for their undergraduate degree. The LSAT has a range of $120180$ and is

scored on a normal distribution with a mean of $151$ and a standard deviation of $9\mathrm{.}6$ points.

College GPAs are also normally distributed with a mean of $3\mathrm{.}35$ and a standard deviation of

$0\mathrm{.}29.$ You may assume that GPA and LSAT are independent of each other.

The vast majority of Harvard Law School students attend an Ivy League school for their

undergraduate program, with many doing their undergraduate at Harvard College. Ivy League

schools require SAT scores, which are also normally distributed. SAT scores range from $400$

$1600,$ with a mean in the US of $1,060$ and a standard deviation of $195.$ The minimum score to be

accepted at an Ivy League school for Undergrad is $1400.$

In the United States, $1,093,234$ individuals play high school football each year. Of those players,

$71,060$ of them will play football in college. Of those who play in college, $853$ will play in the

NFL$.$

If Larry$$s academic and athletic skills are equal, and Larry wants to choose the option that gives

him the highest probability of success at achieving one of his goals, which direction should Larry

choose and why?