Short term versus long run

Short-term aberrations do not affect the long run. To illustrate, suppose that you flip a coin 10 times and you get 10 heads. Find the cumulative proportion of heads, including these first 10 flips, if:

(a) in the 100 flips after those 10 you get 50 heads (so there are now 60 heads in 110 flips),

(b) in the 1000 flips after those 10 you get 500 heads, and

(c) in the 10,000 flips after those 10 you get 5000 heads. What number is the cumulative proportion tending toward as n increases? Hint: Add 10 to both the numerator and the denominator of each ratio and observe the solution from (a) to (c) Use any good applet or simulator from the web.