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Problem of the Week
Problem B and Solution
Pony Up!
Problem
A horse's height h is measured by an ancient unit known as a `hand'.
The measurement is done from the ground to
the withers (the tip of the shoulder blade at the
base of the horse's neck).
Suppose there are two ponies and three horses
in a eld, with heights 12, 13, 14, 15, and 16
hands. If you select four animals randomly,
what is the probability that their average height
is at least 14 hands?
Solution
There are ve dierent ways to select 4
animals, as shown in the table at the right.
Their average heights are also calculated and
shown in the table. For example, the average
of the rst selection is
Selected
Heights
Average
Height
12, 13, 14, 15
13.5
12, 13, 14, 16
13.75
12 + 13 + 14 + 15 54
=
= 13.5 hands.
4
4
12, 14, 15, 16
14.25
The other averages are calculated in a similar
manner.
13, 14, 15, 16
14.5
12, 13, 15, 16
14
Recall that the probability of an event is the ratio
Number of desired outcomes
P=
.
Total number of possible outcomes
Since there are only 3 ways to select 4 animals such that their average height is
3
at least 14 hands, the probability is P = .
5