[gogeo]

You've incorrectly defined the event. You've defined the probability of one coin flip, not six consecutive flips calculated before the first flip.

The sum of the probability of all outcomes equals 1. If you consider that, you'll realize the probability of six correct calls cannot be 50%, because that outcome is no more likely than 6 others...zero correct, one correct, two correct, three correct, etc.

Fail.

[fortheDeclaration]

No, because each coin flip is an event in itself!

There is nothing in the number of coin flips that would dictate any particular result.

It is always 50-50.