A website offers for $1000$ colones, the possibility of playing $4$ shifts a certain game of randomly, in each turn the user will have the same probability $p$ of winning the game and obtaining $1000$ colones (per shift). But to calculate $p$ he asks you to roll $3$ dice and add the results, with what p will be the probability of obtaining this sum. Olcoman visits the website, and upon rolling the dice, he realizes that the probability of losing his money is from $\left( \frac{103}{108}\right)^4$. a) Determine the probability $p$ that Olcoman wins a game and the possible outcomes with the dice, to get to this one. b) Which sums (with the dice) give the maximum probability of having a profit of exactly $1000$ colones? Calculate this probability and the value of $p$ for this case.