Question

Problem 3 in your textbook presents three different sample spaces for a horse race with five horses running. Let the horses be designated by the letters A, B, C, D, and E. A more complete characterization of an outcome of the horse race would be to designate which horse finishes in first through fifth places

(a) Consider the sample space for the set of outcomes characterized in this way. How many such outcomes are in the sample space?
b) How many outcomes are in the event that horse A finishes first?
(c) If G is the event that horse A finishes first and H is the event that horse B does not finish second, describe in words the event GnH. How many outcomes are in this event?

Answer 1

a) 120

b) 24

c) 18

Explanation:

part a

The sample space is defined by the rank of the horses.

Hence, 5 ranks would permute to = 5! = 120 outcomes

part b

Fixing the first position for horse A we are left with four horses and 4 positions, the position are permutated to 4! = 24 outcomes

part c

Fixing the first position for horse A we are left with four horses and 4 positions, and horse B can not finish second hence:

A _ B _ _ the rest can permute hence, 3! = 6 outcomes

A _ _ B _ the rest can permute hence, 3! = 6 outcomes

A _ _ _ B the rest can permute hence, 3! = 6 outcomes

Total outcomes is sum of 3 cases above = 18 outcomes