A manager is attempting to assess the probability of a recession ending in the next six months and its impact on expected profitability. The manager believes there is a $33$ percent chance the recession will end in six months and profits will return to $$100$ million. However, there is a $67$ percent chance the recession will not end in six months, resulting in a $$7$ million loss. The standard deviation of profits over the next six months is

Multiple Choice

$$28\mathrm{.}31$ million.

$$0$ million.

$$57\mathrm{.}40$ million.

$$50\mathrm{.}31$ million.