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

Question

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

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

Bunuel · Accepted Answer

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.

Countdown · Answer

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.

Bunuel · Answer

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.

Asifpirlo · Answer

yes, 1/216

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

so 1/216

hellosanthosh2k2 · Answer

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

Sravan95 · Answer

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,

An78w · Answer

@Banuel - The sum of 3 die can be 3 to 18. Won’t the probability of getting 18 be 1/16 here?

dsteeps · Answer

Great question, thanks for posting!

Bunuel · Answer

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?

An78w · Answer

Absolutely. Thanks!

Posted from my mobile device

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards