Question

The sum of the shown probabilities in the Venn diagram is not equal to 1 because:

A: There is overlap between events
B: the sample space does not have to total 1
C: There are items in the sample space that are neither in event A nor event B
D: There are some items in event B that are not shown

Answer 1

The sum of the shown probabilities in the Venn diagram is not equal to 1 because of overlap between events and because there are items in the sample space that are neither in event A nor event B.

Step-by-step explanation:

A Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events. The sum of the shown probabilities in the Venn diagram is not equal to 1 because of two reasons:

1. There is overlap between events A and B. In the example given, A and B share the outcome 6, which is included in both events. This means that the probability of this outcome is counted twice.
2. There are items in the sample space that are neither in event A nor event B. In the example given, the outcomes 1, 2, 3, 4, and 5 are not part of either event A or event B. Therefore, their probabilities are not included in the sum.