Math Is Fun Forum

tony123

Member

Registered: 2007-08-03

Posts: 229

What is the probability

Rick, Dan and Alan play table tennis with two players at one side of the table and the third one at the other side. Dan and Alan playing together beat Rick three times as often as Rick beats them, Dan wins the game against Rick and Alan as often as he loses it, and Alan wins the game against Rick and Dan twice as often as he loses it. Last time they played six games during the afternoon, two in each arrangement of players. What is the probability that Rick won at least once?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: What is the probability

It's easy enough to verify that the probability of him not winning at all is (3/4 x 1/2 x 2/3)² = (1/4)² = 1/16.

That means the probability of him winning at least once must be 15/16.

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Why did the vector cross the road?
It wanted to be normal.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: What is the probability

I verified mathsy's answer to be correct, but I did it
a harder way using the volumes and areas of when he
does win.  You probably won't get this, but it comes
out to 15/16.
Ricky3Games = [1/3(1-1/8) + 1/4(1-1/6)][1/2] + [1/2][1]
Ricky6Games = [Ricky3Games + Ricky3Games(1 - Ricky3Games)]
I just used the remaining area, like the opposite of the
area and volumes that mathys used, by drawing cubic rectangles
and a square at the end to go from 3 to 6 games.

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