Download Chapter 4.1 Empirical Probability

CHAPTER 4.1
Empirical
Probability
COMPLEMENTARY EVENTS
 The complement of an event E is the set of outcomes
in the sample space that are not included in the
outcomes of event E. The complement of E is
denoted by E
 For example, the complement of rolling a die and
getting an odd number would be
E = 2, 4, 6
FIND THE COMPLEMENT OF EACH EVENT
1. Rolling a die and getting a 4
2. Selecting a letter of the alphabet and getting a
vowel
3. Selecting a month and getting a month that begins
with a “J”.
4. Selecting a day of the week and getting a weekday
PROBABILIT Y OF COMPLEMENTARY
EVENTS
 P(E) = 1 – P(E)
 P(E) = 1 – P(E)
 P(E) + P(E) = 1
RESIDENCE OF PEOPLE
 If the probability that a person lives in a
industrialized country of the world is 1/5, find the
probability that a person does not live in an
industrialized country.
EMPIRICAL PROBABILIT Y
 The difference between classical and empirical
probability is that classical probability assumes that
certain outcomes are equally likely (like when
flipping a coin), while empirical probability, relies on
actual experience to determine the probability to
determine the likelihood of an event.
 Empirical probability is also called experimental
probability
DISTRIBUTION OF BLOOD T YPES:
Blood type
Frequency
A
22
B
5
AB
2
1. P(O)
2. P(A or B)
3. P(not A or O)
4. P(not AB)
O
21
HOSPITAL STAYS FOR KNEE
REPLACEMENT PATIENTS
Find each probability
1. A patient stayed
exactly 5 days
2. A patient stayed
less than 6 days
3. A patient stayed at
most 4 days
4. A patient stayed at
least 5 days
Number of days
stayed
3
Frequency
15
4
32
5
56
6
19
7
5
LAW OF LARGE NUMBERS
 When a coin is tossed one time, it is common
knowledge that the probability of getting heads is ½.
But what if it’s tossed 10 times? Will it come up 5
times heads and 5 times tails?
 Experiment time!