Question

Horse Racing. Each part of this exercise contains from Exercise 5.54. In each case, decide whether the events are mutually exclusive.

Part (a) A and B

Part (B) B and C

Part (C) A,B and C

Part (D) A,B and D

Part (e) A,B,C and D

Short answer

Part (a) A and B are mutually exclusive events.

Part (b) B and C are mutually exclusive events.

Part (c) A, B and C are not mutually exclusive events.

Part (d) A, B and D are mutually exclusive events.

Part (e) A, B,C and D are not mutually exclusive events.

Step-by-step solution

Part (a) Step 1. Given information.

Events.

A ={ 1,3}

B ={ 6,7,8}

C ={ 1,2,3}

D ={ 2,5}

Part (a) Step 2. A and B are mutually exclusive events.

$A\cap B=\varphi$

Because they have no shared outcomes, events A and B are mutually exclusive.

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

$B\cap C=\varphi$

Because they have no shared outcomes, events B and C are mutually exclusive.

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

$A\cap C=3$

The occurrences A, B, and C are not mutually exclusive because a pair of them have similar consequences.

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

$$\begin{gathered} A\cap B=\varphi \\ B\cap D=\varphi \\ A\cap D=\varphi \end{gathered}$$

As a result, A, B, and D are mutually exclusive events.

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

$A\cap C=3$

As a result, A, B, C, and D are not mutually exclusive events.