# Probability

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```					      Probability

Lesson 3: Compound Events

Mrs. Parziale
Probability of Compound Events
Probability = Number of successful outcomes
Total number of outcomes
• Compound Events: Two            or more events
occurring at the same             time.

• Two types of compound events:
– Independent
– Dependent
Independent Events
• The outcome of one event does
not     affect the outcome of the second.

• For two independent events A and B:
P(A and B) =     P(A) · P(B)
Examples
• 1) An urn contains 3 red and 5 blue marbles. What is
the probability of selecting at random, with
replacement, two blue marbles?

• 2) Suppose a number cube is rolled twice. What is the
probability that an odd number will occur both times?
Dependent Events:
• Events where the outcome of one event
does         affect the outcome of
the second event.

• For two dependent events:
P( A and B) = P(A) ·P(B after A occurs)
Examples:
• 1) An urn contains 3 red and 5 blue marbles. What is
the probability of selecting at random, without
replacement, two blue marbles?

• 2) From a club of 25 students, 5 girls and 20 boys, two
students will be randomly selected to serve as president
and vice president. What is the probability that two girls
will be selected?
Mutually exclusive
• Two events can not occur at the same
time    . It involves the    addition   of
each probability.

P(A or B) = P(A) + P(B)
Example
• If one card is selected at random from a
standard deck of 52 cars, what is the
probability of choosing a ten or an ace?
Not Mutually Exclusive
• Two events could occur at the same time
with overlapping components in the
sample space. This is found by:

P(A or B) = P(A) + P(B) – P(overlap)
Example
A spinner is divided into 8 regions number 1-8.
Find P(a multiple of 2 or a multiple of 3).
Example
• Of 3510 drivers surveyed, 1950 were male and 103
were color-blind. Only 6 of the color-blind drivers were
female. What is the probability that a driver was male or
was color-blind?
Closure
• What is a compound event? Give an example.
• Explain the difference between dependent and
independent events.
• What does it mean when two events are
mutually exclusive.
• How do you find the probability of the following:
–   Mutually exclusive event
–   Not mutually exclusive event
–   Two independent events A and B
–   Two dependent events A and B

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 views: 2 posted: 2/12/2013 language: English pages: 12