BRAIN TRIVIA
Logic & Math Puzzle: A coin is flipped 1,000 times. It lands on heads 560 times. Does that sound like a fair coin?
Hint:
A fair coin won’t land on heads exactly 500 times. But it should be close to 500.
To figure out what “close” means, we look at something called the standard deviation, which is the normal amount of variance.
Solution:
When you flip a coin many times, the number of heads will vary a bit. To measure that variance, we use:
Standard deviation = √(number of flips x chance of heads x chance of tails)
For a fair coin:
Chance of heads = 50% or 0.5
Chance of tails = 50% or 0.5
Number of flips = 1000
So:
Standard deviation = √(1000 x 0.5 × 0.5) = 15.8
This means a fair coin should usually land on heads between 484 and 516 times.
But this coin landed on 560 heads, which is way outside of that range. In fact, it’s more than 3 standard deviations above what’s expected.
Final answer
Because 560 is much higher than what a fair coin should produce, the coin probably isn’t fair.