Q1.
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.
Answer
Yes — and the interesting part is where exactly the knowledge stops.
- Your friend knows the complete sample space, S = {H, T}, before the coin leaves your hand.
- Your friend knows each result carries probability 1/2.
- Your friend cannot know which of the two this particular toss will give.
Why it happens: a probability is a statement about the experiment, not about any one trial. Saying P(H) = 1/2 does not half-predict this toss; it says that if the toss were repeated many times, heads would turn up in about half of them. A single trial has no "half" about it — it is either a head or a tail.
Guessing on one toss: chance of being right = 1/2
Guessing on 20 tosses: expected number right ≈ 20 × 1/2 = 10
Guessing on 20 tosses: expected number right ≈ 20 × 1/2 = 10
So your friend will be right about half the time however cleverly they guess — and that is the sharpest sign that the coin is genuinely random. If any guessing rule did better than half in the long run, the coin would not be fair.
Try This: toss the ₹ 1 coin 20 times while your friend calls each toss in advance. Count the correct calls. Repeat with a different guessing rule — always "heads", or alternating H, T, H, T. All the rules will hover near 10 out of 20. The coin cannot be outguessed.