Question

You roll a die with the sample space S = {1, 2, 3, 4, 5, 6}. You define A as {1 ,4, 6}, B as {1, 3, 4, 5, 6}, C as {1, 5}, and D as {2, 3, 5) 5}. Determine which of the following events are exhaustive and/or mutually exclusive
Exhaustive Mutually exclusive
a. A and B (Click to select) (Click to select)
b. A and C Click to select) (Click to select)
c. A and D (Click to select) (Click to select)
d. Band C (click to select) (click to select)

Answer 1

Answer:

Step-by-step explanation:

Recall that two events A,B are called mutually exclusive if and only if $A\cap B = \emptyset$ (their intersection is empty). They are exhaustive if they are mutually exclusive and their union is the sample space.

Based on this

a) Note that $A\cap B = \{1,6\}$, so they are not mutually exclusive nor exhaustive.

b) $A\cap C = \{1\}$ so they are not mutually exclusive nor exhaustive.

c) $A\cap D = \emptyset$, so they are mutually exclusive. Note that $A\cup D = \{1,2,3,4,5,6\}=S$. Then they are exhaustive.

d) $B\cap C = \{1,5\}$, so they are not mutually exclusive nor exhaustive.