Question

Horse Racing.Refer to the image below and for each of the following events, list the outcomes that constitute the events and describe the event in words.

1. (not C)
2. (C & D)
3. (A or C)

Short answer

1. Case (not C) is where the number of the winning horses is more than 3.
2. Case (C & D) is where the number of the winning horses is at most 3 and one of the two long shots the horse has won.
3. Case (A or C) is when the winning horse is either one of the top two favorites or has a number of no more than three.

Step-by-step solution

Part (a)   Step 1.  Given information 

In a horse race, the odds against winning are as shown in the following table:

Horse	#1	#2	#3	#4	#5	#6	#7	#8
Odds	8	15	2	3	30	5	10	5

Events are given by:

$A=\{3,4\},B=\{6,7,8\},C=\{1,2,3\},D=\{2,5\}$

Part  (a)   Step 2. Calculation 

$Samplespace=\{1,2,3,4,5,6,7,8\}$and $C=\{1,2,3\}$

Hence , $(notc)=\{4,5,6,7,8\}$

So, Case (not C) is where the number of the winning horses is more than 3.

Part  (b)  Step 1. Calculation  

As, $C=\{1,2,3\}$and $D=\{2,5\}$

Hence, {2} $(C\&D)=\left\{2\right\}$

So, Case (C & D) is where the number of the winning horses is at most 3 and one of the two long shots the horse has won.

Part (c)  Step 1. Calculation  

As, $A=\{3,4\}$and $C=\{1,2,3\}$

Hence $(AorC)=\{1,2,3,4\}$

So, Case (A or C) is when the winning horse is either one of the top two favorites or has a number of no more than three.