Q1.
Such unpredictability can be useful sometimes! For example, in a cricket match, the fact that a coin is tossed to decide which team will bat first is considered to be a fair method. Can you explain why?
Answer
Because the coin gives both captains exactly the same chance, and gives neither of them any way to influence the result.
Coin is unbiased ⇒ P(Heads) = P(Tails) = 1/2
Captain A's chance of winning the toss = 1/2
Captain B's chance of winning the toss = 1/2
Captain A's chance of winning the toss = 1/2
Captain B's chance of winning the toss = 1/2
Why it happens: a fair method must be equal and uncontrollable. The coin delivers both. It is symmetrical, so there is no physical reason for it to land on one face more often than the other — that is what the book means by unbiased. And a random toss means it is allowed to fall freely, so no skill, strength, seniority or home advantage changes the outcome. Even the choice of who calls does not matter: calling "heads" and calling "tails" both carry probability 1/2.
Here the unpredictability is the whole point. If the result could be predicted or arranged, the stronger side would arrange it. Because nobody can, both teams accept the result before it happens.
Did you know? The same reasoning is used far beyond cricket — drawing lots to break a tie in an election, randomly allotting exam-hall seats, or picking one slip out of a box for the school assembly. In each case fairness comes from every candidate having the same probability, not from anybody being clever.