Monte Carlo simulation provides an easy method for estimating probabilities which are difficult to compute analytically. It is based on the notion that when the simulation is repeated many times, the probability, p, is approximately:

number of successes/number of trials

1. Rolling Two Dice. Estimate the chance of rolling a 7 using two dice. On the TI-82, enter:
   
   seq(iPart(rand*6 + 1), X, 1, 99, 1) sto L1
   
   2nd ENTER sto L2
   
   L1 + L2 sto L3
   
   

   Stat Plot:

   Type = histogramWindow: X [0, 13] Xlist = L3Y [O, 25] Freq = 1Xscl = 1

   
   Move cursor to min = 7 and compute p = n/99
   
   Compare to the theoretical value, p = 1/6.
   
   
2. The Dartboard Problem. A dart board consists of a circle inscribed in a square. If darts are randomly thrown at the board, what is the probability, p, that a dart that hits the board will land within the circle?
   
   Use the TI-82 program DARTS to estimate p. Compare this
   value to the actual probability, p = pi/4.
   
   This simulation can also be used as a method for approximating pi.
   
   
3. The Needle Problem. A needle, length L, is randomly dropped on a surface covered with parallel lines, D units apart. What is the probability, p, that the needle will cross one of the lines?
   
   Run the TI-82 program NEEDLE to estimate the value of
   p. Compare the resulting ratio to the theoretical probability,
   p = 2L/(pi*D).