April 02, 2012
Theoretical Probability
Objective:
Learn to estimate probability using
theoretical methods.
The probability of an event is a number from 0 to 1 (or 0%
to 100%) that tells us how likely the event is to happen.
April 02, 2012
April 02, 2012
Theoretical Probability - is used to estimate
probabilities by making certain assumptions about
an experiment.
Total number of possible outcomes
An experiment is an activity in which results are
observed. Each observation is called a trial, and each
result is called an outcome.
Outcome - result of an experiment.
April 02, 2012
Equally Likely - All of the outcomes have the same probability.
Also, the sum of all the probabilities must add up to 1.
Suppose there are n equally likely outcomes in an
experiment.
· The probability of EACH individual outcome is 1/n.
·
· The probability of an event is
number of outcomes in an event
n
Ex: Are the results of rolling a dice equally likely?
· Find the probability of rolling a 4.
· Find the probability of rolling a 6.
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Compound event is made up of two or more separate
events.
To find the probability of compound events, we first need
to classify them as independent or dependent events.
Independent Event - the occurrence of one event does
NOT affect the probability of the other.
Ex: A coin landing on heads and then landing on tails
on another toss.
Dependent Event - the occurrence of one event DOES
affect the probability of the other.
Ex: Drawing a 6 from a deck of cards and then
drawing a 7.
April 02, 2012
There are 2 red cubes and 2 white cubes in a cup. In each
situation below, the first cube drawn is put back in the cup before
the second draw.
a. If you pull out a red cube first, what is the theoretical probability of getting
a white cube on the second draw? _________
b. If you pull out a white cube on the first draw, what is the theoretical
probability of getting a white cube on the second draw? _________
c. In the above situations, are the events independent or dependent?
______________________
d. What would cause the answer to “c” to be different?
______________________
April 02, 2012
In a bag with 20 marbles, 4 marbles are blue.
a. One marble is drawn from the bag. What is the probability that it is a blue
marble? __________ What is the probability that it is not a blue marble?
___________
b. Suppose a blue marble is drawn on the first draw and it is not replaced.
What is the probability of drawing a blue marble on the second draw?
______________
c. Suppose another color (not blue) is drawn on the first draw and is not
replaced. What is the probability of drawing a blue marble on the second
draw? ___________
d. Is drawing a blue marble on the second draw dependent or independent of
the first draw?
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Impossible Event – A probability of 0 means the event is impossible.
Certain Event – A probability of 1 means the event is certain, or has
to happen.
April 02, 2012
An experiment consists of rolling two fair number
cubes. Find the probability of each event.
a. Probability of rolling a sum of 4
P(sum of 4) = _________________
b. Probability of rolling a sum of 1
P(sum of 1) = _________________
c. Probability of rolling at least one 5
P(at least one 5) = _____________
d. Probability of rolling a 8
P(8) = ______________________
April 02, 2012
Determine if the outcomes of the events described are
equally likely.
a. Rolling an even number on a number cube with sides numbered 1-6 and
rolling an odd number on the same cube ___________________
P(even number) =
P(odd number) =
b. Rolling a number less than 2 on a number cube with sides numbered 1-6
and rolling a number greater than 3 on the same cube
__________________
P(<2) =
P(>3) =
c. Spinning a 1 on this spinner and spinning a 3 on this spinner
___________________
April 02, 2012
Stephany has 2 dimes and 3 nickels. How many pennies should
be added so that the probability of drawing a nickel is 3/7?
Let x equal the number of pennies.
April 02, 2012
What color should you shade the blank region so that the probability of the
spinner landing on that color is 1/2?
B
R
R
B
G
R Y
April 02, 2012