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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posted:2/12/2013
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