The coach of a baseball team wants to know the probability that a particular player hits one home run during a game in which the player goes up to bat 4 times. Based on the player's past games, the coach assumes that the player has a 0.10 probability of hitting a home run in the current game. Because the player will either hit a home run or will not for each time at bat, the coach uses the binomial distribution.
This example uses the binomial distribution. However, you follow these same steps for any distribution that you select.
The probability that the baseball player will hit one home run over 4 attempts is 0.2916. The probability that the player does not hit a home run over 4 attempts is 0.6561. The probabilities of hitting more than one home run during the game are much smaller. For example, the probability that the player will hit a home run each of the 4 attempts is 0.0001.