Simulation

Consider a kicker on a football team who has four chances in one season to make a field goal from less than 30 yards to win the game. At that range, the kicker normally makes 80 % of their field goals.

Without needing to recreate the actual game environment multiple times, the experiment can be simulated by generating random numbers. In this case, the kicker's four attempts will be simulated as four random numbers between 0 and 4. Since the kicker's probability of making a field goal is 80 %, which is four out of five, one out of five numbers will represent a failed attempt. Successful Attempt:& 1, 2, 3,or4 Failed Attempt:& 0 To get more reliable results, the experiment will be repeated 25 times. Imagine the effort needed to have to conducted that in real life! ccccc 1144 & 3441 & 4102 & 0342 & 4320 3032 & 3443 & 2424 & 3000 & 4303 4412 & 0402 & 2414 & 1141 & 0424 2024 & 1302 & 2243 & 2011 & 1111 1132 & 0110 & 0223 & 0202 & 2443 The data set shows several possible outcomes generated by a simulation. Note that the highlighted experiments contain a failed attempt. ccccc 1144 & 3441 & 4102 & 0342 & 4320 3032 & 3443 & 2424 & 3000 & 4303 4412 & 0402 & 2414 & 1141 & 0424 2024 & 1302 & 2243 & 2011 & 1111 1132 & 0110 & 0223 & 0202 & 2443 The set of outcomes shows that 14 trials include at least one failed attempt, meaning there are 11 trials where the kicker made all four field goals. The experimental probability can be calculated using this information. P(4goals out of4attempts) = 11/25 = 44 % The experimental probability that the kicker makes four out of four attempts is 44 %. However, each simulation may give a somewhat different result. The following applet repeats the simulation and calculates the experimental probability of each one.

The applet also records the experimental probabilities of previous simulations.