Question

Horse Racing. In a horse race, the odds against winning are as shown in the following table. For example, the odds against winning are 8 to 1 for horse #1.

List the outcomes constituting.

A = event on e of the top two favorites wins (the top two favorites are the two horse with the lowest odds against winning).

B = events the winning horse's number is above 5.

C = events the winning horse's number is at most 3,that is 3 or less and

D = event on e of the two long shots wins (the top long shots are the two horse with the highest odds against winning).

Short answer

Part (a) possible outcome {3,4}

Part (b) possible outcome {6,7,8}

Part (c) possible outcome {1,2,3}

Part (d) possible outcome {2,5}

Step-by-step solution

Part (a) Step 1. Given information.

The following table shows the odds against winning a horse race:

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

. Part (a) Step 2. Event A's possible outcomes

A race in which one of the top two favourites, i.e. the two horses with the lowest odds against winning, wins. Table 1 shows that horses 3 and 4 have the best lowest odds. Hence

Event A = {3,4}

Part (b) Step 1. Given information.

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

Part (b) Step 2. The possible outcomes of Event 

Event B is the race in which the winning horse has a number greater than 5.

Hence, Event {6,7,8}

Part (c) Step 1. Given information.

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

Part (c) Step 2. Event C's possible outcomes

C is the event in which the number of the winning horse is equal to or less than 3.

Hence, Event {1,2,3}

Part (d) Step 1. Given information.

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

Part (d) Step 2. Event D's possible outcomes

D is the event in which one of the two long shots, i.e. the two horses with the greatest odds of winning, wins. Horses 2 and 5 in Table have the greatest odds.

Hence, Events D = {2,5}