Who has the greatest chance of winning?

Question

In the ironing tip, you must bet the result 1, X or 2 in 13 matches. We assume that there is an equal probability for each event to occur.

a) Niki bets a row with only one and Lucas bets every third 1, X, 2. Who has the greatest chance of winning? Motivate your answer.

b) Maja claims that it is more difficult to get everyone wrong than everyone right. Is it true? Motivate your answer.

Answer 1

Then the probability of win is 1/3 while probability of loss is 2/3 each and every guess.

So in 13 trials, the expected number of wins is 4.

They have an equal probability

the probability of getting all N trials correct is (1/3)^N = 1/(3^N)

while the probability of getting all N trials wrong is (2/3)^N = 2^n/ 3^n

so 1/3^n vs (2^n) / 3^n ... which one do YOU think is more likely?