-Distribution of sum- Monty Hall Parody Suppose that in a television show you've won three blank vouchers $$S_a,S_b,S_c$$ with total amount $600$ euro. The stage has three doors $A,B,C$ which opened with keys $a,b,c$ respectively. Behind the door $A$ stand operator who turns voucher $S_a$, into $S_a$ cash. Behind the door $B$ stand operator who turns voucher $S_b$ into $5\cdot S_b$ ​​cash. Behind the door $C$ stand operator who turns voucher $S_c$ into $2\cdot S_c$ ​​cash. Moderator of the show then ask you to choose one of three keys $a,b,c$ . The question is how we should distribute the amount acquired through vouchers for the most money, despite the choice of the key.

The sum we split in the parts by proportion $$S_a:S_b:S_c=1:1/5:1/2$$ $$S_a+S_b+S_c=600$$ $$S_a/1=S_b/(1/5)=S_c/(1/2)=k$$ $$k+k/5+k/2=600$$ $$k=6000/17=352,94$$ $$S_a=352,94,S_b=70,58,S_c=176.47$$