Data Sufficiency

In a certain game of dice, the player's score is determined as a sum of three throws
of a single die. The player with the highest score wins the round. If more than one
player has the highest score, the winnings of the round are divided equally among
these players. If Jim plays this game against 21 other players, what is the
probability of the minimum score that will guarantee Jim some monetary payoff?


The QA [spoiler]1/216[/spoiler]

Can anybody pls explain how to solve this one?

GMAT Hacker wrote:In a certain game of dice, the player's score is determined as a sum of three throws
of a single die. The player with the highest score wins the round. If more than one
player has the highest score, the winnings of the round are divided equally among
these players. If Jim plays this game against 21 other players, what is the
probability of the minimum score that will guarantee Jim some monetary payoff?


The QA [spoiler]1/216[/spoiler]

Can anybody pls explain how to solve this one?

Only way the minimum score that will guarantee Jim some monetary payoff is to get highest score (Since even if of all other 21 players get highest score Jim will still get portion of the winning amount). Highest score would be to get 6 on each of the three throws..
so for each throw the probability to get 6 is 1/6 , for each throw (3 independent events multiplied) 1/6*1/6*1/6 = 1/216

Imagibe Jim is the first guy to throw the dices. Now inorder to have some monteary pay off. he needs to get maximun score which is 6 + 6 + 6 = 18

Now probability of getting 6 is 1 /6

hence probability of getting 6 + 6 + 6 = 1/6 * 1/6 * 1/6 = 1/216

hi.itz.mani wrote:Imagibe Jim is the first guy to throw the dices. Now inorder to have some monteary pay off. he needs to get maximun score which is 6 + 6 + 6 = 18

Now probability of getting 6 is 1 /6

hence probability of getting 6 + 6 + 6 = 1/6 * 1/6 * 1/6 = 1/216

Thnx Both of you:)