Is it a fair coin ?

[Tomm]

Suppose Ignatius from his pocket took out a coin which he knew was a fair coin. He tossed it 40 times - he got 18 heads and 22 tails.
Remember - it's a fair coin, not a trick coin, there is nothing unusual with
it. All is fine with the result.

Now Ignatius got another coin, we don't know whether this one is
a fair coin or not. It has not been disclosed whether it's a fair coin or not.

Now we are going to find out more about it. This time Ignatius tossed it 40000 times. What did he get ? He got 18000 heads and 22000 tails.

Paul said: "The result tells me it can't be a fair coin."
John said "There's nothing unusual about the result. It's a fair coin."
While Mary said: "There's no definite answer because it's basically unpredictable.
How could coin tosses be predictable ?"

Whom do you agree with ?

 

[Tomm]

Please guess.

 

[Tomm]

Only 1 of them is correct, which of them ?

You will discover something from the answer which insurance people know since long ago.

 

[MotherFirefly]

Unpredictable, since he could have used a trick coin?

 

[Tomm]

Certainly it's possible. That's what's the riddle is asking you: whether it's a fair coin or not ??

Now the answer: Paul is correct, because it is not a fair coin. This answer is supported by a mathematical law - the Law of Large Numbers.

Can we be so certain ? Yes - if the Law of Large Numbers is not trustworthy, then the insurance industry wouldn't have survived. The same goes for the casinos.

The world is more amazing and complex than we think.

 

[HarvestTheFields]

Certainly it's possible. That's what's the riddle is asking you: whether it's a fair coin or not ??

Now the answer: Paul is correct, because it is not a fair coin. This answer is supported by a mathematical law - the Law of Large Numbers.

Can we be so certain ? Yes - if the Law of Large Numbers is not trustworthy, then the insurance industry wouldn't have survived. The same goes for the casinos.

The world is more amazing and complex than we think.

Yep, there's a reason investors diversify their portfolios.

 

[Tomm]

It can also be proved with Binomial distribution and Chi square.

When we calculate the probability using Chi square, the answer is so small, that it's almost zero.