College Algebra & Trigonometry, 2018a

7.6. PROBABILITY 331
7.6 Probability
If a coin is tossed three times, what is the probability of getting exactly two heads?
at least two heads? no heads?
Probability is defined as the number of ways the event in question can happen
divided by the number of total possibilities. We can define the collection of all
possible outcomes in an experiement with all outcomes equally likely as the sample
space of the experiment. Then the number of ways the event in question can
happen can be defined as n(E) and size of the sample space can be defined as
n(S). In this notation, the probability of an event P (E) is defined below:
P (E) = n(E)
n(S)
=
number of elements in E
number of elements in S
The question at the opening of this section addresses a situation in which a coin
is tossed three times. We can use a tree diagram to examine the sample space of
this situation.
H
H
T
H
T
H
T
T
H
T
H
T
H
T
The possibilities in this experiment are:
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT }
Since there are eight possibilities, with 3 of them having exactly two heads, the
probability is 3 8 =0.375.