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

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Intern
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GMAT Date: 08-25-2013
In a certain game of dice, the player’s score is determined [#permalink]

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New post Updated on: 14 Aug 2013, 01:13
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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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Re: In a certain game of dice, the player’s score is determined [#permalink]

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New post 14 Aug 2013, 01:16
6
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.

Answer: C.

Hope it's clear.
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Re: In a certain game of dice, the player’s score is determined [#permalink]

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New post 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.

Answer: C.

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.

Thanks in advance.
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Re: In a certain game of dice, the player’s score is determined [#permalink]

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New post 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.

Answer: C.

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.

Thanks in advance.


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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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 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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New post 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.

Answer: C.

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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In a certain game of dice, the player’s score is determined [#permalink]

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New post 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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