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Ilya T.2021-08-10 22:15:06
Probability theory
Ilya T., 2021-08-10 22:15:06

What do I understand wrong in the puzzle about the cube?

In one game, they asked a problem:


Alice is playing a game of chance in which dice must be rolled until a minimum predetermined score limit is reached.
The dice in the game are six-sided, for one roll you can get [1, 6] points. When, after a roll, the sum of the dice exceeds the minimum threshold, the game ends. If, as a result, the number of points scored does not exceed the maximum specified limit, then Alice wins
. The number of dice in the game is unlimited. Calculate the probability that Alice wins
Input:
min_goal, max_goal - lower and upper bounds. If Alice gets min_goal <= x <= max_goal points, then she wins
Conclusion:
float - chance to win the jackpot, round the result to hundredths

Example:
min_goal = 2
max_goal = 6
get_result(min_goal , max_goal ) = 0.91
On the first throw, you can get a number from 1 to 6. If 2-6 falls out, then Alice immediately wins, if 1 falls out, then you have to roll the die again and then there is a chance to lose if 6 falls out


I try to solve on the numbers from the example and immediately fall into a stupor. In my understanding, this is solved as follows: out of all possible combinations of two dice (which are 6 * 6 = 36), we lose in 1 case when the first one is 1 and the second is 6. That is. probability of losing 1/36 and winning 35/36 = 0.97(2)
Where did they get 0.91?

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