Suppose we have a coin that comes up heads with probability 2/3 independently every time we flip it. What is the most likely sequence to observe if we flip it 100 times?

Step-by-step explanation: The coin comes up heads with probability of 2/3, or 0.66. It doesn't depend on how many times you flip it, which means that the second flip doesn't depend on the result of the first one.

if you throw the coin 100 times, you most likely will see that the coin comes up heads most of half the times, exactly 2/3 of the total throws.

it is because each flip is independent of the previous one, so the probability in one is the first same the third or the fourth.