MathDB

LR2

Part of 2019 Costa Rica - Final Round

Problems(1)

3 dice game

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2019 Shortlist LC2 day1 (logical reasoning)

9/22/2021
A website offers for 10001000 colones, the possibility of playing 44 shifts a certain game of randomly, in each turn the user will have the same probability pp of winning the game and obtaining 10001000 colones (per shift). But to calculate pp he asks you to roll 33 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 (103108)4\left( \frac{103}{108}\right)^4. a) Determine the probability pp 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 10001000 colones? Calculate this probability and the value of pp for this case.
probabilitycombinatorics