[phys_08]

Dave has a coin. One side of it is a picture of a duck, and the other side of it is the maple leaf. For dinner tonight, he can’t decide whether he wants to have a burger or roast chicken, so he decides to let chance pick for him. However, he has a hunch that the coin is weighted. In order to ensure a fair chance of picking burger or roast chicken, he decides to toss the coin 9 times and pick the outcome that occurs the most times: If he gets more maple leaves, he’ll have burger, and if more ducks, roast chicken. The question is, is his method good enough to ensure he gets an unbiased result? Please explain your reasoning.

[Stratmando]

If weighting the coin increase the odds, then odds are whichever it lands on the most out of nine, would be my Bet.

[Unknown008]

Yup, say the probability of the coin for falling on the maple leaf is 1/3 instead of 1/2 and that on the duck is 2/3 instead of 1/2, then, as you increase the number of tosses, the number of maple leaves divided by the number of ducks will tend to be 1:2, that is more ducks will be obtained and is therefore not biased.

If however he tosses it a mimimum time, it'll be further away from the ratio of 1:2. So, either he gets an unbiased coin, or tosses it once.

That's my bet ;)