Objective To differentiate between probability and relative frequency and to solve problems involvin

1
Objective- To differentiate between probability
and relative frequency and to solve problems
involving both.
If a woman were to have a baby in 1990, what is
the probability that it would be a boy?
of favorable outcomes
Probability
of possible outcomes
1
boy
P (boy)

50
boy or girl
2
Probability involves predicting future events.
2
Probability involves predicting future events.
Relative Frequency involves data from past events.
of times an event occurred
Relative Frequency
of times it could have occurred
of boys born in 1990
2,129,000
r

0.512
total of births in 1990
4,158,000
r 51.2
Based on relative frequency, the probability of
having a boy is actually 51.2.
3
In 1990, the state of Illinois tested 3840 skunks
for rabies, of which 1446 actually had rabies.
What was the relative frequency of skunks with
rabies?
frequency
1446
r

0.377
total opportunities
3840
r 37.7
4
If a hurricane is likely to occur on any day of
the week, what is the probability that it
will occur on a weekend?
of days in weekend
2

P (hurricane)
of days in week
7
2
0.286 or 28.6
7
5
Probability and relative frequency are
always expressed as fractions ( or decimals )
between 0 and 1.
Probability-future
certain
impossible
Relative Frequency-past
always occurred
never occurred
6
Complementary Events
Two events are complementary if
their intersection is the empty set and
their union is the set of all possible outcomes.
Complementary
P(Hurricane on weekend) P(Hurricane on
weekday)

1
The sum of probabilities for complementary
events always equals 1.
P(It will rain) P(It will not rain)
30 70
100