An example of probabilities in a coin-tossing experiment

Question

Illustrates an example of probabilities in a simple coin-tossing experiment.

Answer 1

Probabilities in a simple coin-tossing experiment: one toss.

Above shows the distribution for the above coin-tossing experiment.

Now here's what your total profit will be like after one thousand tosses as in figure. Your expected profit after one toss is

(1/6) x 10 + (5/6) x (-1) = 5/6 ≈ 0.833

Now variance is as:

(1/6) x (10 - (5/6))²+ (5/6) x (-1-5/6)² = 605/54