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In a certain game of dice, the player’s score is determined

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Intern
Joined: 16 Jan 2013
Posts: 22
Concentration: Finance, Entrepreneurship
GMAT Date: 08-25-2013
In a certain game of dice, the player’s score is determined  [#permalink]

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Updated on: 14 Aug 2013, 01:13
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Question Stats:

75% (01:53) correct 25% (02:00) wrong based on 175 sessions

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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?

A. 41/50
B. 1/221
C. 1/216
D. 1/84
E. 1/42

Originally posted by Countdown on 13 Aug 2013, 21:39.
Last edited by Bunuel on 14 Aug 2013, 01:13, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 02 Sep 2009
Posts: 54440
Re: In a certain game of dice, the player’s score is determined  [#permalink]

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14 Aug 2013, 01:16
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Countdown 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?

A. 41/50
B. 1/221
C. 1/216
D. 1/84
E. 1/42

To guarantee that Jim will get some monetary payoff he must score the maximum score of 6+6+6=18, because if he gets even one less than that so 17, someone can get 18 and Jim will get nothing.

P(18)=1/6^3=1/216.

Hope it's clear.
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Intern
Joined: 16 Jan 2013
Posts: 22
Concentration: Finance, Entrepreneurship
GMAT Date: 08-25-2013
Re: In a certain game of dice, the player’s score is determined  [#permalink]

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14 Aug 2013, 03:29
Bunuel wrote:
Countdown 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?

A. 41/50
B. 1/221
C. 1/216
D. 1/84
E. 1/42

To guarantee that Jim will get some monetary payoff he must score the maximum score of 6+6+6=18, because if he gets even one less than that so 17, someone can get 18 and Jim will get nothing.

P(18)=1/6^3=1/216.

Hope it's clear.

Bunnel thanks for posting the answer

But can you make one point clear that the question asks for the "minimum value". Won't this make any change while deciding the choices.

Math Expert
Joined: 02 Sep 2009
Posts: 54440
Re: In a certain game of dice, the player’s score is determined  [#permalink]

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15 Aug 2013, 03:40
Countdown wrote:
Bunuel wrote:
Countdown 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?

A. 41/50
B. 1/221
C. 1/216
D. 1/84
E. 1/42

To guarantee that Jim will get some monetary payoff he must score the maximum score of 6+6+6=18, because if he gets even one less than that so 17, someone can get 18 and Jim will get nothing.

P(18)=1/6^3=1/216.

Hope it's clear.

Bunnel thanks for posting the answer

But can you make one point clear that the question asks for the "minimum value". Won't this make any change while deciding the choices.

Not sure I understand your question...

Anyway, minimum score Jim should have to guarantee that he will get some monetary payoff is 18 (maximum possible). No other score will guarantee him that.
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Posts: 312
Re: In a certain game of dice, the player’s score is determined  [#permalink]

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15 Aug 2013, 05:41
Countdown 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?

A. 41/50
B. 1/221
C. 1/216
D. 1/84
E. 1/42

yes, 1/216

1 = 6+6+6, it ensures money.
every possibility = 6×6×6 = 216

so 1/216
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Re: In a certain game of dice, the player’s score is determined  [#permalink]

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01 May 2015, 07:57
Bunuel wrote:
Countdown 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?

A. 41/50
B. 1/221
C. 1/216
D. 1/84
E. 1/42

To guarantee that Jim will get some monetary payoff he must score the maximum score of 6+6+6=18, because if he gets even one less than that so 17, someone can get 18 and Jim will get nothing.

P(18)=1/6^3=1/216.

Hope it's clear.

Hi Bunnel

Is there no significance of mentioning the number of players as 21 in the question ?
As GMAT questions always have every information worthy
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Joined: 02 Apr 2014
Posts: 477
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
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In a certain game of dice, the player’s score is determined  [#permalink]

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16 Aug 2017, 21:21
Hi Bunel,

One question, it is mentioned that a player victory is found by sum of number on die on three throws.
So there 6 x 6 x 6 possible outcomes, but outcomes {1,2,3},{1,3,2},{2,1,3},{2,3,1},{3,1,2},{3,2,1} ..all these combinations will add up to 6, so there 3! repetitions, so shouldn't we divide (6 x 6 x 6)/3! ? actually i was looking for answer 1/36 based on above logic. Please correct me if wrong
In a certain game of dice, the player’s score is determined   [#permalink] 16 Aug 2017, 21:21
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