Experimental Probability of Compound Events

Warm Up A dentist has 400 male and female patients that range in ages from 10 years old to 50 years old and up as shown in the table. What is the experimental probability that the next patient will be female and in the age range 22–39?

A compound event is an event that includes two or more simple events, which can be dependent on each other or independent. Recorded data can be used to find the experimental probability of a compound event. A simulation or model of an experiment can be used to find the experimental probability of compound events. To find the experimental probability of a compound event? Write a ratio of the number of ways the event happens in an experiment to the total number of times the experiment was performed.

A compound event is an event defined by two or more separate simple events, such as rolling a 1 and a 2 when rolling two different number cubes. This is different from an event that is defined by two or more outcomes, such as rolling a 1 or a 2 when rolling a single number cube. In probability, two events are independent if the occurrence of one does not affect the probability of the occurrence of the other. If events are not independent, they are dependent. These definitions lead to two different multiplication rules for the theoretical probability of events A and B. For independent events, P(A and B) = P(A) x P(B). For dependent events, P(A and B) = P(A) x P(B|A), where P(B|A) denotes the probability of event B given the occurrence of event A. Sometimes it can be difficult to determine whether events are independent or not. In these cases, the multiplication rules can be used to confirm or deny independence.

A restaurant offers white, multigrain, or rye toast with its regular or deluxe breakfasts. A server records in the table the orders she gets one morning. What is the experimental probability that the next customer wants rye toast with a deluxe breakfast? That the next customer chooses multigrain toast with a regular breakfast?

A breakfast cart offers plain and multigrain bagels with three different toppings: butter, cream cheese, or jam. The orders one morning were recorded in the table. What is the experimental probability that the next customer wants a multigrain bagel with cream cheese?

To find the probability of a compound event using data recorded from an experiment or a simulation, first find the total number of trials in the experiment. Then, find the number of occurrences of the compound event. The experimental probability is the ratio of the number of occurrences to the total number of trials.

At a deli, a customer can choose a roll or crackers to have with soup At a deli, a customer can choose a roll or crackers to have with soup. The customer can choose tomato, vegetable, or chicken noodle soup. Customers choose each possibility with about the same frequency. Use a simulation to find the experimental probability that the next customer will have a roll with vegetable soup.

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