We will toss a six-sided die. The sample space of outcomes from this dice toss is S = {1, 2, 3, 4, 5, 6}. Consider the following events:
A = the result is an even number = {2, 4, 6}
B = the result is at least four = {4, 5, 6}
Which outcomes are in the event A^C?
The event A^C represents the complement of event A, which means it includes all outcomes that are not in event A.
Since event A consists of even numbers {2, 4, 6}, the event A^C will include all outcomes that are not even numbers. In other words, it will include all odd numbers.
Therefore, the outcomes in event A^C are: {1, 3, 5}.
To find the outcomes in the event A^C, we need to determine the outcomes that are not in event A.
Event A represents the set of even numbers: A = {2, 4, 6}.
The complement of event A, denoted as A^C, consists of all outcomes in the sample space that are not in event A.
Since the sample space S = {1, 2, 3, 4, 5, 6}, we can list the outcomes that are not in event A:
A^C = {1, 3, 5}
Therefore, the outcomes in the event A^C are 1, 3, and 5.
To find the outcomes in the event A^C, we first need to understand what A^C represents.
The notation A^C represents the complement of event A. In other words, it represents all the outcomes that are not in A.
Since event A consists of even numbers {2, 4, 6}, the complement of A would be all the outcomes that are not even numbers.
Since our sample space is S = {1, 2, 3, 4, 5, 6}, we need to determine which outcomes in S are not in the event A.
From the sample space, we can see that the odd numbers are {1, 3, 5}. These odd numbers are not in the event A because A consists only of even numbers. Therefore, the outcomes in the event A^C are {1, 3, 5}.