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?

Step-by-step solution

Idea: A method is fair when every side has the same chance. A fair coin gives heads and tails the same chance, and the result cannot be predicted, so the toss gives both teams an equal chance.

1. Outcomes of the toss: heads or tails. A fair coin is symmetrical, so there is no reason for it to land on one side more often than the other. The two outcomes are equally likely: P(heads) = P(tails) = 12.½ mark
2. One captain calls (say, heads). The captain wins the toss if the coin shows heads and loses if it shows tails. So each captain has a chance of 12 of winning the toss.½ mark
3. Nobody can predict or control the result. The coin is tossed freely into the air, so neither captain, nor the umpire, can make it land a particular way. The result is decided by chance alone.½ mark
4. Since both teams have the same chance and nobody can influence the result, neither team gets an unfair advantage in choosing to bat or bowl first. That is why the toss is considered fair. Here unpredictability is useful: it is exactly what makes the decision fair.½ mark

Check: If the coin were bent so that it showed heads 70% of the time, the captain who called heads would have a 0.7 chance and the other only 0.3. The method would then be unfair. So fairness depends on the outcomes being equally likely.

Answer to write in the exam

Common mistakes that cost marks

• Saying “it is fair because the toss is quick” or “because it is a tradition”. The real reason is the equal chance (12 each) and the fact that nobody can control the result.
• Thinking the team that won the last toss is less likely to win this one. Each toss is a fresh start; the coin has no memory, so the chance is still 12.
• Forgetting the word fair (unbiased) coin. A bent or weighted coin would not give an equal chance.

How this can come in the exam

Try one yourself

Three friends want to decide who sits in the front seat. Would tossing one coin be a fair method for three people? Suggest a fair method.

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