- #1
mathmari
Gold Member
MHB
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Hey! ![Eek! :eek: :eek:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
I am looking the following:
I am looking the following:
- There are 1 Million voters. 2000 of them know exactly that they will vote for A, but the other 998000 will decide if whether they will vote for A or B in the voting booth using a coin.
With which possibility will A get more votes?
- At a quiz we get 20.000 Euro. We have the chance to increase the money tenfold. For this we have to find out from 7 boxes, the one which contains the number '10'.
We can unpack 2 boxes. However, if we are unlucky and cannot find the '10', the 20.000 euros will go as well lost.
But can can not participate in the game and take the 20.000 euros home.
How do we decide when we join the game once and what strategy do we use if we play every year?
- Suppose that the voters vote for a if at tossing a coin they get head. So that A wins we have to get such a number of heads that \begin{align*}&2000 + \text{ number of heads }> 998000 - \text{ number of heads } \\ & \Rightarrow 2\text{ number of heads }>998000-2000 \\ & \Rightarrow 2\text{ number of heads }>996000 \\ & \Rightarrow \text{ number of heads }>498000\end{align*}
So, the possibility that will A win is equal to the possibility that we get more that $498000$ times "head", or not? (Wondering) - Do we choose one of the two correct boxes out of 7 with probability $\frac{2}{7}$ ? (Wondering)