1.6 KiB
id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f5221000cf542c510033 | Problem 436: Unfair wager | 5 | 302107 | problem-436-unfair-wager |
--description--
Julie proposes the following wager to her sister Louise.
She suggests they play a game of chance to determine who will wash the dishes.
For this game, they shall use a generator of independent random numbers uniformly distributed between 0 and 1.
The game starts with S = 0.
The first player, Louise, adds to S different random numbers from the generator until S > 1 and records her last random number '$x$'.
The second player, Julie, continues adding to S different random numbers from the generator until S > 2 and records her last random number '$y$'.
The player with the highest number wins and the loser washes the dishes, i.e. if y > x the second player wins.
For example, if the first player draws 0.62 and 0.44, the first player turn ends since 0.62 + 0.44 > 1 and x = 0.44. If the second players draws 0.1, 0.27 and 0.91, the second player turn ends since 0.62 + 0.44 + 0.1 + 0.27 + 0.91 > 2 and y = 0.91. Since y > x, the second player wins.
Louise thinks about it for a second, and objects: "That's not fair".
What is the probability that the second player wins? Give your answer rounded to 10 places behind the decimal point in the form 0.abcdefghij
--hints--
unfairWager() should return 0.5276662759.
assert.strictEqual(unfairWager(), 0.5276662759);
--seed--
--seed-contents--
function unfairWager() {
return true;
}
unfairWager();
--solutions--
// solution required