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

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

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] New post   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.

Answer: C.

Hope it's clear.
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In a certain game of dice, the player’s score is determined [#permalink] New post   16 Aug 2017, 21:21
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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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Re: In a certain game of dice, the players score is determined [#permalink] New post   04 Oct 2022, 12:12
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An78w wrote:
@Banuel - The sum of 3 die can be 3 to 18. Won’t the probability of getting 18 be 1/16 here?



When you roll 3 dice you can have the following sums: 3 (min possible 1+1+1), 4, 5, 6, ...., 18 (max possible 6+6+6), so total of 16 possible sums. But the probabilities of these sums are not equal, so it's not 1/16 for each. That's because not all scores from 3 to 18 have equal number of ways to occur: you can get 10 in many ways but 3 or 18 only in one way only (3=1+1+1 and 18=6+6+6).

Does this make sense?
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Re: In a certain game of dice, the player’s score is determined [#permalink] 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] New post   15 Aug 2013, 03:40
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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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Re: In a certain game of dice, the player’s score is determined [#permalink] 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] New post   09 Nov 2020, 10:56
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.


Hai, I have a similar doubt.
If the dice is rolled 3 times, the possible scores range from 3 to 18 ( a total of 16 different numbers)
Hence, the probability of obtaining 18 as sum will be 1/16.
Please clarify my reasoning.

Thanks & Regards,
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Re: In a certain game of dice, the players score is determined [#permalink] New post   04 Oct 2022, 11:23
@Banuel - The sum of 3 die can be 3 to 18. Won’t the probability of getting 18 be 1/16 here?
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Re: In a certain game of dice, the players score is determined [#permalink] New post   04 Oct 2022, 11:29
Great question, thanks for posting!
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Re: In a certain game of dice, the players score is determined [#permalink] New post   04 Oct 2022, 12:34
Absolutely. Thanks!

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