Question

If you flip a fair coin and get heads 10 times in a row, what is the chance of getting tails on the next flip? Explain.

Answer 1

There is an 1/2 chance to get a head of a coin each time. To get 10 heads in a row, an 1/2 chance has to be multiplied for 10 times. So, the formula to complete the coin scam on the first attempt is (1/2)10. As a result, the chance of DB completing the coin scam on the first attempt is 1/1024.

The grey traces (representing nH−nT) are a Bernoulli random walk. If you think of a particle moving up or down the y-axis by a unit step (randomly with equal probability) at each time-step, then the distribution of the position of the particle will 'diffuse' away from 0 over time.

nH-nT=0.5

10-nT=0.5

T=10.5/11

=0.9545

The chance of getting tails on the next flip is 0.9545.