Page 16 - Probability Demystified

CHAPTER 1 Basic Concepts 5

SOLUTION:

There are 8 + 5 + 3 + 4 = 20 outcomes in the sample space.
8 2
a. PðredÞ¼ ¼
20 5
3 þ 4 7
b. Pðblack or pinkÞ¼ ¼
20 20
8 þ 3 þ 4 15 3
c. P(not yellow) = P(red or black or pink) ¼ ¼ ¼
20 20 4
0
d. P(orange)= ¼ 0, since there are no orange jellybeans.
20

Probabilities can be expressed as reduced fractions, decimals, or percents.
For example, if a coin is tossed, the probability of getting heads up is 1 or
2
0.5 or 50%. (Note: Some mathematicians feel that probabilities should
be expressed only as fractions or decimals. However, probabilities are often
given as percents in everyday life. For example, one often hears, ‘‘There is a
50% chance that it will rain tomorrow.’’)
Probability problems use a certain language. For example, suppose a die
is tossed. An event that is specified as ‘‘getting at least a 3’’ means getting a
3, 4, 5, or 6. An event that is specified as ‘‘getting at most a 3’’ means getting
a1,2,or3.

Probability Rules

There are certain rules that apply to classical probability theory. They are
presented next.

Rule 1: The probability of any event will always be a number from zero to one.

This can be denoted mathematically as 0 P(E) 1. What this means is that
all answers to probability problems will be numbers ranging from zero to
one. Probabilities cannot be negative nor can they be greater than one.
Also, when the probability of an event is close to zero, the occurrence of
the event is relatively unlikely. For example, if the chances that you will win a
certain lottery are 0.00l or one in one thousand, you probably won’t win,
unless of course, you are very ‘‘lucky.’’ When the probability of an event is
1
0.5 or , there is a 50–50 chance that the event will happen—the same
2