% Set up boxes

p = [0.8; 0.15; 0.05];
X = [10; 30; 80];

Target_Value = 20;

%% Reduce smallest probability

% assume boxes are ordered
assert(p(1) > 0);
assert(X(1) < Target_Value);
assert(Target_Value < X(2));

% E = p1*X1 + p2*X2 + (1-p1-p2)*X3
if Target_Value < X(2)
    % We can obtain Target_Value with positive p1.
    c = (p(2)*X(2) + (1-p(1)-p(2))*X(3) - (1-p(1))*Target_Value) / p(1) / (Target_Value - X(1));
    p(1) = c*p(1);
end
p = p / sum(p);

E = p'*X;


>> E

E =

   20.0000

>> p

p =

    0.6923
    0.2308
    0.0769