Ask your friend to predict the outcome of a ₹ 1 coin you toss. Do you see that your friend could guess heads or tails but could not know for certain? That’s randomness! All possible results are known, but each individual try is unpredictable.

Step-by-step solution

Idea: Do the activity several times and keep a record. If your friend could really know the result, every guess would be right. In fact about half the guesses are right, just as chance alone would give.

1. The possible results are known: the ₹ 1 coin can land heads (H) or tails (T). Your friend always guesses one of these two.½ mark
2. Try it 10 times and record. One sample run:
   Guess: H, T, H, H, T, T, H, T, H, T
   Result: T, T, H, T, H, T, H, H, T, T
   Correct guesses: tosses 2, 3, 6, 7 and 10, that is 5 out of 10. (Your own numbers will be different.)½ mark
3. Your friend is right sometimes and wrong sometimes, with no way of telling in advance which. On each toss the chance of a correct guess is 12, so over many tosses about half the guesses are right.½ mark
4. So your friend could guess but could not know for certain. All possible results are known, but each individual toss is unpredictable. That is exactly what randomness means.½ mark

Check: In the sample run, 5 correct out of 10 gives a relative frequency of 510 = 0.5, matching the chance of 12 for a correct guess.

Answer to write in the exam

Common mistakes that cost marks

• Thinking that after several heads in a row, tails is “due”. The coin has no memory; the chance of tails is still 12 on every toss.
• Concluding from a few lucky guesses that your friend can predict the coin. Getting 3 or 4 right in a row happens by chance; over many tosses the success rate settles near half.
• Saying the result is unpredictable because the outcomes are unknown. The outcomes (H, T) are known; only which one will occur is unknown.

How this can come in the exam

Try one yourself

Aman guessed the result of 12 coin tosses and was right 7 times. What fraction of his guesses were right? Does this mean he can predict coin tosses?

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