The value $($in $ $)$ of a share per unit develops, apart from the constant factor $10,$ according to a geometric Brownian motion $\{x(t),t0\}$ given by

$x(t)=10e^{B(t)},0t120,$

where $\{B(t),t0\}$ is the Brownian motion process with volatility $=0\mathrm{.}1.$

At time $t=0$ a speculator pays $$17$ for becoming owner of a unit of the share after $120[$days$],$ irrespective of the then current market value of the share.

$(1)$ What will be the mean undiscounted profit of the speculator at time point $t=120?$

$(2)$ What is the probability that the investor will lose some money when exercising at this time point?

In both cases, take into account the amount of $$17,$ which the speculator had to pay in advance.