Question

Dice. Refer to exercise 5.53.

a Are events A and B mutually exclusive?

b Are events B and C mutually exclusive?

c Are events A, C and D mutually exclusive?

d Are there three mutually exclusive events among A, B, C and D? four?

Short answer

Part (a) A and B are not mutually exclusive because they have similar consequences.

Part (b) B and C are mutually exclusive.

Part (c) A, C, and D are not mutually exclusive

Part (d) A,B, C, and D are not mutually exclusive

Step-by-step solution

Part (a) Step 1. Given information.

A = {2,4,6}

B = {4,5,6}

C = {1,2}

D = {3}

Part (a) Step 2. A and B are not mutually exclusive events.

A and B are not mutually exclusive because they have similar consequences.

$(A\cap B)=\{4,6\}$

Part (b) Step 1. Events B and C are mutually exclusive 

Because they have no common outcomes, the occurrences B and C are mutually exclusive.

$(B\cap C)=\varphi$

 Part (c) Step 1. A, B and D are not mutually exclusive events. 

The occurrences A, C, and D are not mutually exclusive because they have similar results.

$(A\cap C)=2$

 Part (d) Step 1.The events A, B, C, and D are mutually exclusive in three or four ways.

There are three mutually exclusive events among the occurrences A, B, C, and D because no two of them have the same outcome.

Events A, B, C, and D are not mutually exclusive because a pair of them have the same outcome.

$$\begin{gathered} (A\cap B)=\{4,6\},(B\cap C)=\varphi ,(C\cap D)=\varphi ,(A\cap B)=\{4,6\},(B\cap C)=\varphi \\ (C\cap D)=\varphi \\ (A\cap C)=\left\{2\right\},(A\cap D)=\varphi ,(B\cap D)=\varphi ,(A\cap C)=\left\{2\right\},(A\cap D)=\varphi (B\cap D)=\varphi \end{gathered}$$