Let the values of the dice in a roll be $a$ and $b$. You win money if ($1$) $a$ and $b$ are both even, ($2$) $a$ is even and $b$ is odd with $a&gt;b$, or ($3$) $a$ is odd and $b$ is even with $a&lt;b$.
For ($1$) there are $3$ even numbers in $1,2,\dots,6$, so there are $3^2=9$ ways for $a$ and $b$ to both be positive.
For ($2$) consider the three cases cases: $a=2 \implies b=1$; $a=4\implies b=1,3$; and $a=6\implies b=1,3,5$. Therefore, there are $6$ ways to get condition ($2$).
Condition ($3$) is the same as ($2$) by symmetry, so the probability to win money is
$$
\frac{3^2 + (2)(6)}{6^2} = \frac{21}{36} = \frac{7}{12}.
$$
We can easily generalize this to any $n$-faced pair of dice when $n$ is even. Notice that the triangular numbers appear when counting conditions ($2$) and ($3$). Therefore, the general probability is
$$
\frac{(n/2)^2 + 2T_{n/2}}{n^2} = \frac{n + 1}{2n}.
$$

What is the probability that Brian makes money on his first roll


In a work place PC has a data acquisition card which is 16 bit and has 16 single ended channels. One of the channels is outputting a constant DC voltage which can be controlled by a user via a program in the PC. 

The output voltage is feeding a VFD. The VFD takes the voltage value and controls the frequency of the AC motor depending on the voltage applied.

There is an isolation amplifier between DAQ analog output and the VFD as in the figure. 
When I measure the analog output of the DAQ and the output of the isolation amplifier with a voltmeter I see the same value.

What might be the reason then for this amplifier?
