Which of the following is an example of an independent event?
A. choosing one sock at random from your drawer, putting it on, and then choosing another at random
B. flipping a coin and rolling a number cube
C. choosing students at random for basketball teams
D. removing a marble from a bag, and then choosing another without replacing the first
D. removing a marble from a bag, and then choosing another without replacing the first is an example of an independent event. The probability of selecting the second marble does not depend on the outcome of the first marble selected.
To determine which of the options is an example of an independent event, we need to understand what an independent event is.
An independent event is an event where the outcome of the first event does not affect the outcome of the second event. In other words, the probability of the second event remains the same regardless of what happens in the first event.
Now, let's analyze the options:
A. Choosing one sock at random from your drawer, putting it on, and then choosing another at random:
In this case, the probability of choosing the second sock is not affected by the outcome of the first sock. So, this is an example of an independent event.
B. Flipping a coin and rolling a number cube:
In this case, flipping a coin and rolling a number cube are two separate events. The outcome of flipping a coin does not impact the outcome of rolling a number cube. Therefore, this is also an example of an independent event.
C. Choosing students at random for basketball teams:
This scenario involves choosing multiple students at random. However, the probability of choosing the second student is affected by the outcome of the first student chosen. So, this is not an example of an independent event.
D. Removing a marble from a bag, and then choosing another without replacing the first:
In this case, the probability of choosing the second marble is affected by the outcome of the first marble being removed. The fact that the first marble is not replaced changes the probability for the second event. Therefore, this is not an example of an independent event.
Based on the analysis, options A and B are both examples of independent events.