The world's largest library of math and science simulations.

Next Monday is the first collegiate football national championship in the 12-team playoff era. Sometimes, the outcome of a football game can come down to the narrowest of margins, even to the flip of a coin to determine who gets the ball first.



The probability of choosing the correct outcome of the flip is 0.5, or 50%. This is true of all fair coins, no matter how many times the coin is flipped. When the first event does not affect the probability of the second event, they are independent events. In contrast, if you are playing cards, the probability of drawing an ace from the deck depends on how many aces have been drawn before. Picking a second ace becomes less likely after the first ace is drawn, so these events are dependent.



In the Independent and Dependent Events Gizmo, students explore independent and dependent events by drawing colored marbles from a bag. The marbles are either replaced after each draw (independent event) or not replaced (dependent event). After each simulation, students compare experimental probability to theoretical probability.



Enjoy the game, and good luck to both teams!