Question

If I tell you that I have a coin, but it is a special coin. In that, I mean that it is not a 50/50 coin. However, I don't know how likely it is for it to land on heads (or tails). So we decide to flip it 10 times and we get 40% heads (which is 0.40 as a proportion). Are you willing to say that it is a 40/60 coin? Why or why not?

after we flipped it 10 times and got 40% heads, a friend of ours comes up and we tell him what we are doing. He says, "What happens if we flip it 10 times again?" We do and get 30% heads (a proportion of 0.30).

**Is this something that you would expect to happen? Why are we getting different proportions of heads? Will we be able to tell how likely it is for the coin to be on heads?**

Answer 1

No, we can't say it is 40/ 60 coin.

Because we only flip it 10 number of times, which is very small.

Yes because we are tossing it less number of times and aggregate percentage is achieve only in large number of trials as empirical definition of probability says.

Not now,

we are able to say how likely to be a head.

After tossing infinite(large) number of times we get a sequence of probabilities and this sequence converges on a value .

Then we say that is the probability of getting head.