Let's consider an image which is either Truck or Car.
<p>
If you report that the probability of Truck is q, 
there will be 1 − (1 − q)<sup>2</sup> chance of winning $5 if it is a Truck; 
and 1 − q<sup>2</sup> chance of winning the $5 if it is a Car.
</p>

<p>
Why should you truthfully report?
</p>


<p>
Suppose you actually think the probability of a Dog is &pi;, which does not necessarily equal to q, then your overall probability of getting $5 is 
</p>

<p>
(1 − (1 − q)<sup>2</sup>)*&pi; + (1 − q<sup>2</sup>)*(1-&pi;)
</p>

After doing some math, you will see that it is maximized when q = &pi;.