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Probability of winning at least two games in a row - - - Elementary Probability

checkittwice

Member
Apr 3, 2012
37
You can play against player A or player B in an all-skill game
(such as chess or checkers).

Suppose there are no ties/draws.

On average you beat player A 90% of the time in this game,
and on average you beat player B 10% in this game.

You will play three games in row, and each game will be
against one player at a time.


You will choose one of these scenarios:


1st game - - a game against player A
2nd game - - a game against player B
3rd game - - a game against player A


OR


1st game - - a game against player B
2nd game - - a game against player A
3rd game - - a game against player B


-------------------------------------------------------------------------------------


Which scenario should you choose to have the greatest
chance of winning at least two games in a row? * *







** This is adapted from a problem presented by Martin Gardner.

 

CaptainBlack

Well-known member
Jan 26, 2012
890
You can play against player A or player B in an all-skill game
(such as chess or checkers).

Suppose there are no ties/draws.

On average you beat player A 90% of the time in this game,
and on average you beat player B 10% in this game.

You will play three games in row, and each game will be
against one player at a time.


You will choose one of these scenarios:


1st game - - a game against player A
2nd game - - a game against player B
3rd game - - a game against player A


OR


1st game - - a game against player B
2nd game - - a game against player A
3rd game - - a game against player B


-------------------------------------------------------------------------------------


Which scenario should you choose to have the greatest
chance of winning at least two games in a row? * *







** This is adapted from a problem presented by Martin Gardner.

The second.

Construct a contingency tree to investigate further.

In both such trees there is a branch where the first two games are won, this branch occurs with probability \(0.09\) (the outcome of the third game does not effect the probability of winning two games in a row along this branch).

The other main branch involves loseing the first game and winning the remaining two. This occurs with probability \(0.1 \times 0.1 \times 0.9\) in the first case and \(0.9 \times 0.9 \times 0.1\) in the second.


CB