Answer:
Since events A and B are mutually exclusive, this means that they cannot occur simultaneously. In other words, the probability of both events A and B happening at the same time (P(A and B)) is 0.
Given:
�
(
�
)
=
0.65
P(A)=0.65
�
(
�
)
=
0.25
P(B)=0.25
�
A and
�
B are mutually exclusive events
We are asked to find:
�
(
�
and
�
)
P(A and B)
�
(
�
or
�
)
P(A or B)
Construct a Venn Diagram
Let's solve each part:
�
(
�
and
�
)
P(A and B):
Since A and B are mutually exclusive,
�
(
�
and
�
)
=
0
P(A and B)=0.
�
(
�
or
�
)
P(A or B):
Since A and B are mutually exclusive,
�
(
�
or
�
)
=
�
(
�
)
+
�
(
�
)
P(A or B)=P(A)+P(B).
�
(
�
or
�
)
=
�
(
�
)
+
�
(
�
)
=
0.65
+
0.25
=
0.9
P(A or B)=P(A)+P(B)=0.65+0.25=0.9
Constructing a Venn Diagram:
Since A and B are mutually exclusive, they do not overlap in the Venn diagram.
Circle A represents event A with a probability of 0.65.
Circle B represents event B with a probability of 0.25.
Since A and B do not overlap, the overlap region (intersection) is empty.
Here's how the Venn diagram looks:
In the Venn diagram:
Circle A represents event A.
Circle B represents event B.
The overlap region is empty since A and B are mutually exclusive.
