We are asked to find an example of a compound event composed of two overlapping events when we spin a spinner divided into 8 parts with the integers from 1 to 8.
A compound event consists of two or more events linked by either the word and or the word or. We want to choose two linked overlapping events. Let A denote the event that we obtain an even number when spinning the spinner.
Favorable Outcomes
2 4 6 8
We will now choose the second event B so that events A and B have at least one outcome in common. Consider the numbers greater than 4. We can see that both 6 and 8 are even numbers that are also greater than 4. Therefore, let B denote the event that we obtain a number greater than 4.
Event A
Event B
Definition
Obtaining an even number
Obtaining a number greater than 4
Spinner Outcomes
2, 4, 6, or 8
5, 6, 7, or 8
We can now write our compound event.
Compound Event (AorB)
We spin an even number or a number greater than 4.
Probability of the Compound Event
We can find the probability of the compound event. To do so, let's start by finding P(A) and P(B). Let's evaluate the probability of event A. Recall that there are exactly 4 even numbers out of 8 possible outcomes that are equally likely.
P(A) = 4/8 = 1/2
Next, let's calculate the probability of event B. Keep in mind that there are exactly 4 possible outcomes that are greater than 4.
P(B) = 4/8 = 1/2
Since events A and B are overlapping, we will use the Probability of Overlapping Events rule to calculate P(AorB).
P(AorB)=P(A)+P(B)-P(AandB)
We have already calculated both the probability of event A and the probability of event B, so all that is left is to find P(AandB). Recall that 6 and 8 are the only outcomes that are even numbers and numbers greater than 4. Therefore, there are 2 favorable outcomes.
P(AandB) = 2/8 = 1/4
Finally, we can calculate P(AorB).
