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

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13 Aug 2013, 21:39

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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?

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.

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.

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.

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.
_________________

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

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

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17 Aug 2014, 07:02

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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.

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

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

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08 Jan 2017, 15:48

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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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

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