For a certain set of carnival games (Games 1-6), the probability of a

Question

For a certain set of carnival games (Games 1-6), the probability of a game being won is perfectly negatively correlated to the value of the reward for winning.

Game 1 has the second-highest probability of being won. 
 Game 2 has the second-lowest probability of being won. 
 The value of the rewards for Games 4 and 6 are between the values for Games 1 and 2. 
 Game 5 has a lower-value reward than does Game 2. 
 No two games have the same probability of being won.

Based on the information provided and from among the six carnival games, select for Highest the game with the highest probability of being won, and select for Lowest the game with the lowest probability of being won. Make only two selections, one in each column.

MartyMurray · Accepted Answer

We are told the following:

For a certain set of carnival games (Games 1-6), the probability of a game being won is perfectly negatively correlated to the value of the reward for winning.

That information means that, without exception, the higher the probability of a game being won, the lower is value of the reward for winning that game. It also means that the lower the probability of a game being won, the higher is the value of the reward for winning that game.

Thus, if we know where in the order the value of reward for winning a game is, we also know where in the order the probability of winning that game is.

Based on the information provided and from among the six carnival games, select for Highest the game with the highest probability of being won, and select for Lowest the game with the lowest probability of being won. Make only two selections, one in each column.

A straightforward way of finding the answer to this question is to create six slots in which we can rank the games from highest to lowest probability of being won in accordance with the provided information.

1.
2.
3.
4.
5.
6.

• Game 1 has the second-highest probability of being won.

1.
2. Game 1
3.
4.
5.
6.

• Game 2 has the second-lowest probability of being won.

1.
2. Game 1
3.
4.
5. Game 2
6.

• The value of the rewards for Games 4 and 6 are between the values for Games 1 and 2.

This information is about the values of rewards. At the same time, since reward value is negatively correlated with probability, it also means that Games 4 and 6 also lie between Games 1 and 2 in the ranking or probability of being won.

1.
2. Game 1
3. Game 4 or 6
4. Game 4 or 6
5. Game 2
6.

• Game 5 has a lower-value reward than does Game 2.

This choice is a little tricky because we are ranking games in order of probability of being won, but this choice is about value of reward. So, we have to be careful to rank Game 5 above Game 2 in our order of probability of being won since reward and probability of being won are negatively correlated.

Meanwhile, since Game 1 has the second highest probability of being won and Game 2 has the second lowest, there are only two slots between the two games, and those slots are already occupied by Game 4 and Game 6.

So, the only possible slot for Game 5 above Game 2 is the top slot.

1. Game 5
2. Game 1
3. Game 4 or 6
4. Game 4 or 6
5. Game 2
6.

• No two games have the same probability of being won.

If no two games have the same probability of being won, the only possible slot for Game 3 is the last slot.

1. Game 5
2. Game 1
3. Game 4 or 6
4. Game 4 or 6
5. Game 2
6. Game 3

So, the game with the highest probability of being won is Game 5, and the one with the lowest is Game 3.

Correct Answer   Game 5, Game 3

KarishmaB · Answer

Perfectly negatively correlated means a correlation of -1. So if one increases, the other will certainly decrease and vice versa. 
"Probability of winning" is perfectly negatively correlated with "Value of reward". So if it is easier to win, the reward is smaller - makes sense.

Let's put them in order (High to Low). No two games have the same probability of being won so we have 6 distinct positions. I would put hyphens in blanks to show the relative positioning of Probbaility of being won. 
 
   Game 1 has the second-highest probability of being won.    
_
_ 1
_
_
_
_
 
   Game 2 has the second-lowest probability of being won.    
_
_ 1
_
_
_2
_
 
   The value of the rewards for Games 4 and 6 are between the values for Games 1 and 2.

If rewards are between 1 and 2, then probability of being won is also between 1 and 2 because of perfect correlation.   
_
_ 1
_ 4/6
_ 4/6
_2
_
 
   Game 5 has a lower-value reward than does Game 2.    
A lower value reward means higher probability of being won. The only blank left above 2 is the top position.

_ 5
_ 1
_ 4/6
_ 4/6
_2
_

Then we must have 3 at the bottom.

_ 5
_ 1
_ 4/6
_ 4/6
_ 2
_ 3

ANSWER: Highest Probability is for Game 5. Lowest Probability is for Game 3

Gemmie · Answer

Probability of being won (highest to lowest) 
Game 1      2nd
Game 2      5th
Game 3      6th (the remaining)
Game 4      either 3rd or 4th
Game 5      1st (lower value mean higher probability)
Game 6      either 3rd or 4th

Game 5: highest
Game 3: lowest

rohanbnj · Answer

got this question in a mock, got it wrong
came back and solved it again now (I had forgotten the question, so was approaching it fresh) and got it right

under time pressure and stress of an exam setting I got it wrong, but got it right when relaxed at home

how to get something like this right, on test day?

Purnank · Answer

Probability of a game being won is perfectly    negatively correlated    to the value of the reward for winning.

Ranks (High to low) 1 2 3 4 5 6
Probability of winning 1st  G5   2ndG1 5thG2 6th  G3  
Rewards for winning  G3  G2 G4/G6 G6/G4 G1  G5 (only possible place for G5 as G5 lower value reward than G2)

1st - G5
2nd - G3

ubaid009 · Answer

adjusting the probablity of winning the game in increasing order as given in the statement
___< game2(Game 2 has the second-lowest probability of being won) < Game4 or Game 6 <Game6 or Game4< Game 1(2nd highest probability) <____.
As Game 5 has a lower-value reward than does Game 2 so, it has high probability of winning the game than Game2. only the Highest probability place is vacant. Hence, highest probabilty of winning the game must be game5. and we are rest with Game 3 and one vacant space i.e. lowest winning probability position

kanikaa9 · Answer

I quickly made this table and could solve it under 1 minute

iantGMAT · Answer

I like to approach these kind of questions with a graph:

- There’s a negative correlation between probability of winning and reward, so draw a negative gradient line.

- Plot Game 1 and Game 2 on the line, leaving a space for the highest and lowest winning probability games

- Game 4 and 6 sit somewhere between 1 and 2 on the line

- Game 5 is lower reward than 2, so will lie to the left of it

This leaves game 3 with the lowest probability of being won, so game 5 must be the highest.

nandini14 · Answer

I still do not understand the positions of 4 and 6

Bunuel · Answer

Here’s the key point about Games 4 and 6:

The problem says  “The value of the rewards for Games 4 and 6 are between the values for Games 1 and 2.”  
 Since reward and win probability are perfectly negatively correlated, that also means their win probabilities must lie between the probabilities of Games 1 and 2.

So, if you imagine the line from highest win% (lowest reward) down to lowest win% (highest reward):

Game 1 is second-highest probability. 
 Game 2 is second-lowest probability. 
 That leaves open slots for the true highest (left of Game 1) and the true lowest (right of Game 2). 
 Games 4 and 6 must occupy positions somewhere between Game 1 and Game 2, not above 1 and not below 2.

They don’t have fixed exact spots, just constrained to be between those two.

For a certain set of carnival games (Games 1-6), the probability of a

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