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In the game of Funball, each batter can either hit a home

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In the game of Funball, each batter can either hit a home [#permalink]

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New post 29 Jul 2006, 22:08
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In the game of Funball, each batter can either hit a home run, hit a single, or strikeout, and the likelihood of each outcome is completely determined by the opposing pitcher. A Funball batter scores a point for their team by advancing sequentially through each of four "bases", according to the following rules:

Home run: The batter and any players already on a base advance through all four bases.
Single: The batter advances to first base, and any players already on a base advance one base each.
Strikeout: No one advances any bases, and the batter loses his/her turn.

If the batting team has a runner on first base, which pitcher (Roger or Greg) is more likely to allow a point before recording a strikeout?

(1) Greg is twice as likely as Roger to allow a single, and four times as likely as Roger to record a strikeout.

(2) Greg is twice as likely as Roger to allow a single, and one fourth as likely as Roger to allow a home run.

(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient

Detailed Explanations appreciated.
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Re: DS: Funball [#permalink]

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New post 30 Jul 2006, 22:49
IMO A...but if have to solve this within 2min, I'd choose E as soon as I read the question...nasty question.. took me over 5min to think what I should do.

Let single = s, homerun=r, strikeout=o

S1. Gs = 2Rs and Go = 4Ro
possible scenarios not to score a point before strikeout
o
s-o
s-s-o

!P(G) = Go+Gs*Go+Gs*Gs*Go
!P(R) = Ro+Rs*Ro+Rs*Rs*Ro = Ro(1+Rs+Rs^2)
!P(G) = 4Ro+2Rs*4Ro+2Rs*2Rs*4Ro = 4Ro(1+2Rs+4Rs^2)

!P(G)-!P(R) = 4Ro(1+2Rs+4Rs^2) - Ro(1+Rs+Rs^2)
= Ro(3+7Rs+15Rs) > 0
Thus, Roger is more likely to allow a score. sufficient.

S2. Gs=2Rs and Gh=(1/4)Rh
possible scenarios to score a point before strikeout
s-s-s-o
s-s-h-o
s-h-o
h-o
P(G) = Gs*Gs*Gs*Go + Gs*Gs*Gh*Go + Gs*Gh*Go + Gh*Go
= 2Rs*2Rs*2Rs*Go + 2Rs*2Rs*(1/4)Rh*Go + 2Rs*(1/4)Rh*Go + (1/4)Rh*Go
P(R) = Rs*Rs*Rs*Ro + Rs*Rs*Rh*Ro + Rs*Rh*Ro + Rh*Ro
Seems we need Ro and Go to solve this.. insufficient not 100% sure
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Re: In the game of Funball, each batter can either hit a home [#permalink]

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New post 05 Jul 2016, 23:03
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Re: In the game of Funball, each batter can either hit a home   [#permalink] 05 Jul 2016, 23:03
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