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A game is played with a six sided, regularly numbered fair die. A player starts with a number equal to \(0.1n,\) where n is an integer between \(1\) and \(6\) inclusive. On each of \(20\) subsequent rolls, if the number rolled times \(0.1\) is greater than or equal to the players current number, the players current number is incremented by \(0.1;\) if the number rolled times \(0.1\) is less than the player's current number and is odd, the players number is decremented by \(0.1;\) if the number rolled times \(0.1\) is less than the player's current number and is even, the players number is unaffected. If \(55\%\) of the die rolls in a particular game are even, which of the following is a possible final value of that game?
I. \(0.8\)
II. \(0.5\)
III. \(0.1\)
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III
The OA is D
A game is played with a six sided, regularly numbered fair die. A player starts with a number equal to \(0.1n,\) where n is an integer between \(1\) and \(6\) inclusive. On each of \(20\) subsequent rolls, if the number rolled times \(0.1\) is greater than or equal to the players current number, the players current number is incremented by \(0.1;\) if the number rolled times \(0.1\) is less than the player's current number and is odd, the players number is decremented by \(0.1;\) if the number rolled times \(0.1\) is less than the player's current number and is even, the players number is unaffected. If \(55\%\) of the die rolls in a particular game are even, which of the following is a possible final value of that game?
I. \(0.8\)
II. \(0.5\)
III. \(0.1\)
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III
The OA is D
