#1. The most likely colour of the second marble is white.

#2. There are 4 possible outcomes for the two marble draw without replacement:

Majority marble, Majority marble

Majority marble, Minority marble

Minority marble, Majority marble

Minority marble, Minority marble

The probablity of these are :

12/20 x 11/19 = 0.3474

12/20 x 8/19 = 0.2526

8/20 x 12/19 = 0.2526

8/20 x 7/19 = 0.1474

SUM =1=P

The P of a Major coming out second is

(12/20 x 11/20) + (8/20 x 12/19) = 0.6000

The P of a Minor coming out is

1 - P(Maj) = 1 - 0.6000 = 0.4000

The first marble drawn was White,

and the P of drawing a Maj in the first draw is 12/20 = 0.6000,

hense the P of White being the Maj is also 0.6000.

It has been shown that that the porobabilty of drawing a Maj in the second draw is also 0.6. In deed, in the absence of information of what has already been draw, the P of drawing a Maj in any/every draw is always 0.6

Therefore the chance of the second marble being White is also 0.6000

Sorry Barry, your flipped coin and going against your instinct means the laser fitted sharks have just made yum cha of your girlfriend.