I don't understand this question below. Help me, please!!! Thank you for helping me!

Question

Suppose you flip a two-sided coin 100,000 times and get heads 75,000 times. Is this coin fair? Why or why not?

Answer 1

Probably Not. That looks suspicious, especially if the other guy is winning bets off you or off someone.

100,000 flips, 75,000 heads is 3/4 heads when you expect much closer to 1/2 heads

Pr(H) = 1/2 mean heads is np = 100,000(1/2) = 50,000

standard deviation is sqr(npq) = sqr(n(p)(1-p)) = sqr(100,000(1/2(1/2) = sqr(100,000(1/4) = sqr(25,000) = 50sqr10= about 158.11

z score = 75,000-50,000)/158.1= 25,000/158.1 = 158.1

nearly zero chance of getting more than z>3. z=158.13 is not believable if the coin was fair. It's a risk we can take, up there with odds of getting struck by lightening, if you get out of bed in the morning.

But in defense of the fair coin hypothesis (which you usually reject if z>2), it is possible for a fair coin to land heads every time for 100,000 times or forever. The only sure way to know is physically examine the coin, somehow weigh it and and see if the head side is less heavy than the tails side. But nothing is certain in life so even that wouldn't actually settle it, for certain.