Simple Probability

Probabilities are numbers between 0 and 1. If the probability that event A occurs is 1, event A will occur. If the probability that event A occurs is 0, event A will not occur. If the probability that event A occurs is 1/2 then there is a 50-50 chance that event A will occur. Although probabilities are numbers we often speak of probabilities as if they were percents.

The symbol P(A) is read "The probability of event A"

If P(A)=1 event A will occur.
If P(A)=0 event A will not occur.

Some probabilities are easy to determine.

Suppose a fair coin is tossed one time.
Then P(getting a head) = 1/2 or 0.5

Suppose a fair die is tossed one time.
P(getting a five) =1/6= 0.166

Probabilities are assigned to events. The probability of an event A is given by the formula


For example, Suppose a die is tossed one time. The number rolled could be a
1,2,3,4,5,or 6. The total number of outcomes is 6, and the number of outcomes that include 5 is exactly 1. So,
P(5)=1/6=0.166

The total set of outcomes is called the Sample space for an event.
The sample space for tossing a fair coin twice or two fair coins is given below.

coin #1coin #2
HH
HT
TH
TT

The probability of getting two heads is: P(HH)=1/4= 0.25

Often we are concerned with the probability that the event A will not occur.
The symbol P(~A) is read "The probability of not A "or "the probability of the complement of A."

P(~A)=1 - P(A)

From the two coin problem above, the probability of not getting two heads is:
P(~HH) = 1 - P(HH) = 1 - 1/4 = 3/4 = 0.75