A solar panel production factory is located in an area subject to occasional flooding. You have been brought in as a consultant to determine whether flood$-$proofing of the building is economically justified. The alternatives are as follows:

Option A$.$ Do nothing. Damage in a moderate flood is $$10,000$ and in a severe flood, $$25,000$;

Option B$.$ Install the stormwater pump at a cost of $$15,000$ to withstand moderate flooding without damage and to withstand severe flooding with $$10,000$ damages;

Option C$.$ Install the stormwater pump and upgrade the sewage system at a cost of $$30,000$ to withstand a severe flood without damage;

Based on the above information, solve problem $1.$

$1.$In any year, the chance of no flooding is $0\mathrm{.}22$ and the chance of moderate flooding is $0\mathrm{.}44.$

What is the expected cost of option B$?$