Question

I toss a penny and observe whether it lands heads up or tails up. Suppose the penny is fair, that is, the probability of heads is 1/2 and the probability of tails is 1/2. This means
A. every occurrence of a head must be balanced by a tail in one of the next two or three tosses.
B. if I flip the coin many, many times, the proportion of heads will be approximately 1/2, and this proportion will tend to get closer and closer to 1/2 as the number of tosses increases.
C. regardless of the number of flips, half will be heads and half will be tails.
D. all of the above.

Answer 1

Now Imo A isn't true since if you throw it 1000 times the first 500 could be tails, and the next could be heads.

B sonds the most correct.

C doesn't always have to be true, because the proportion after 1000 flips could be 502 to 498 which is still about 50%.

D I don't think so

@CliffSedge

Answer 2

B is the only correct choice.

Answer 3

Thank you, that's what I figured as well.

Answer 4

You're welcome :)

Answer 5

Law of large numbers, I think.