Download Empirical Probability

12.1, 12.2
Probability –
Experiment-
Outcomes-
Event-
P(E) =
Empirical Probability-
P(E) =
Ex. A coin is tossed 50 times and landed on heads 27 times. Find the empirical probability of
the coin landing heads up.
Theoretical Probability-
P(E) =
Ex. A coin is flipped. What is the theoretical probability that it will land on heads?
Ex. A die is rolled. What is the probability of rolling:
a) a 5? _______
b) an even number?_______
c) a number greater than 3_______
The law of large numbers-
The probability of an event that cannot occur is ______.
The probability of an event that must occur is ______.
Every probability is a number between 0 and 1 inclusive; that is, 0 ≤ P(E) ≤ 1.
The sum of the probabilities of all possible outcomes of an experiment is ______.
P(A) + ________________
P(not A) = _____________
If 1 card is randomly selected from the deck, find the probability that the card selected is:
a) 7 ______
b) Not a 7______
c) Jack or club ______
d) Heart or club ______
e) Card greater than 5 and less than 8_______
f) Not a jack or a club _______
g) An ace of spades ________
h) Heart and a club ________
Practice Problems
1) A pair of fair dice is rolled 50 times and the sum of the dots on the faces is noted.
Compute the empirical probability that the sum rolled is greater than 9.
2) A die is rolled 100 times with the following results.
Compute the empirical probability that the die comes up 2 or 3.
3) The table shows the number of college students who prefer a given pizza topping. Use the
table to find the following. Round the indicated probabilities to the nearest thousandth.
a) Determine the empirical probability that a junior prefers meat toppings.
b) Determine the empirical probability that a freshman prefers cheese toppings.
c) Determine the empirical probability that a student prefers meat toppings.
4) The Amboy Kennel Club has held an annual dog show for the last 42 years. During this time
the winner of "Best of Show" has been an Alaskan Malamute 21 times, a Great Pyrenees 3
times, and an Siberian Husky 18 times. Determine the empirical probability that the next
winner of "Best of Show" will be a Great Pyrenees.
5) A survey was done at a mall in which 2000 customers were asked what type of credit card
they used most often. The results of the survey are shown in the figure below. Determine the
empirical probability that a person selected at random from the 2000 surveyed uses
Mastercard. Round to the nearest thousandth when necessary.
Find the probability.
6) A bag contains 7 red marbles, 9 blue marbles, and 6 green marbles. What is the probability
of choosing a blue marble?
7) One digit from the number 9,848,558 is written on each of seven cards. What is the
probability of drawing a card that shows 5?
8) Two fair 6-sided dice are rolled. What is the probability the sum of the two numbers on the
dice is 4?
9) Determine the probability that the spinner lands on grey.
10) If a person is randomly selected, find the probability that his or her birthday is in May.
Ignore leap years. Assume that all days of the year are equally likely for a given birth.
11) A class consists of 65 women and 18 men. If a student is randomly selected, what is the
probability that the student is a woman?
12) A fair die is rolled. What is the probability of rolling a 3 or a 4?
13) A fair die is rolled. What is the probability of rolling an odd number or a number less than
3?
14) A spinner has regions numbered 1 through 21. What is the probability that the spinner will
stop on an even number or a multiple of 3?
15) A card is drawn at random from a standard 52-card deck. Find the probability that the
card is not a queen.
16) If a person is randomly selected, find the probability that his or her birthday is not in May.
Ignore leap years.
17) The distribution of B.A. degrees conferred by a local college is listed below, by major.
What is the probability that a randomly selected degree is not in Mathematics? Round to the
nearest thousandth.