Minority wins!

Probability Level 2

Three boys having names $\small{\color{#69047E}John}$ , $\small{\color{#EC7300}Alex}$ and $\small{\color{#20A900}Tom}$ play a game in which -

They have to choose a color from the set of two colors- $\small{\color{#D61F06}RED}$ and $\small{\color{#3D99F6}BLUE}$ .
The one who is in minority on the basis of choice wins.
$\small{\color{#69047E}John}$ and $\small{\color{#EC7300}Alex}$ always oppose each other.

If the probability of a tie in the game (all 3 choose the same color) is $a$ ,
and the probability of $\small{\color{#20A900}Tom}$ losing the game is $b$ ,
then enter your answer as $a+b$ .

1

\frac{1}{2}

\frac{1}{3}

0

1 solution

Shreyansh Mukhopadhyay
Feb 3, 2018

We know that there are three players who have to choose either of the two colors and John and Alex always oppose each other.

So by Pigeonhole principle aleast 2 of them chose the same color, but John and Alex both cannot be together.

That means that one of the two who chose the same color is Tom. So Tom is in the majority. Cosequently he always loses.

Minority wins!

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