Theoretical Probability
Recall: Experimental probability only gives an estimate of the likelihood that a particular will occur.
Note: The probability of an event occurring will always be between __________________________.
Sample Space is the collection of all possible outcomes of the experiment and is denoted by S.
Event Space is the collection of outcomes that correspond to the event of interest and is denoted by A.
Note that event space is a subset of sample Space.
Theoretical probability: when all the outcomes of an event are equally likely, the probability is the ratio of
the number of outcomes that make up that event to the total number of possible outcomes.
Theoretical probability is calculated using the formula: P ( A) 
n(A) and n(S) are the numbers of elements in the two sets.
Ex. 1: If a coin is flipped, find P(Tails)?
Ex. 2: If a single die is rolled, determine the probability of
a) rolling an odd number?
b) rolling a number greater than 4?
c) not rolling a number greater than 4?
n ( A)
n (S )
Ex. 3: If two six sided dice are rolled, Find the probability that
1
2
3
4
5
1
2
3
4
5
6
c)
a)
a sum of 11 is rolled
b)
doubles were rolled
6
a sum other than 11 is rolled
The complement of a set, A, is written as A' and consists of all the outcomes in the sample space that are
not in set A. A' = {outcomes in S that are not in A}
Probability of complementary event:
.
Ex. 4: Assuming we have a standard deck of cards.
a) What is the probability of drawing an ace?
b) What is the probability of drawing anything but an ace?
Ex. 5: Find the probability that one randomly drawn integer between 1 and 49 (inclusive) is NOT a perfect
square.
Homework: Pg218: #1-14.