Rock, Paper, Scissors, Seagull

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Rock, Paper, Scissors, Seagull

In a normal game of rock, paper, scissors, two players simultaneously make a rock symbol (clenched fist), a paper symbol (hands flat) or scissors symbol (index and middle finger extended) with their hand. The winner is determined as follows: rock beats scissors, scissors beats paper, and paper beats rock.

Two players decide to extend the game to include a seagull (thumb and pinky extended as wings), and the seagull can beat the rock or the paper (I'll leave it to your imagination how), and scissors beats seagull.

If the two players both choose the same symbol, it counts as a round in which nobody wins.

The two players play 3 rounds. Player one chooses randomly whether to select rock, paper, scissors, or seagull, and player two always chooses scissors.

Then they play another 3 rounds, in which player one continues to choose randomly, but player two always chooses rock.

What is the probability that player two will win at least 2 of the 3 games in both sets of three?

Presentation mode

Problem by Mr. Twitchell

Solution

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