20) B

Since the balls are arranged in a way to give the smallest possibility for a player to win, the first bag must have 2 red balls and 1 yellow ball and 1 blue ball. The second bag must have 2 red balls and 2 yellow balls.

**Probability of choosing either bag = 1/2**

Let us say a player picked bag 1.

The only way to win is to pick 2 red balls.

Probability of picking a red ball = 2/4 = 1/2

In order to win, the player must pick a second red ball.

Probability of picking a second red ball = 1/3

**Probability of picking two same coloured balls from Bag 1 = 1/2 x 1/2 x 1/3 = 1/12**

Let us say a player picked bag 2.

Only way to win is to either pick 2 red balls or 2 yellow balls.

1st ball

Probability of picking a first red ball = 2/4 = 1/2

Probability of picking a first yellow ball = 2/4 = 1/2

2nd ball

If the player picked a red ball first, they must pick a red ball again if they want to win.

Probability of picking a second red ball = 1/3

If the player picked a yellow ball first, they must pick a yellow ball again if they want to win.

Probability of picking a second yellow ball = 1/3

**Probability of picking two same coloured balls from Bag 2 = 2( 1/2 x 1/2 x 1/3 ) = 1/12 x 2 = 2/12**

There are three possibilities to win:

**2 red balls from bag 1 = Probability of 1/12**

**2 red balls from bag 2 = Probability of 1/12**

**2 yellow balls from bag 2 = Probability of 1/12**

Probability of winning = (1/12 x 3) = 3/12 = 1/4

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