Probability

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Probability

• Week 5

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Probability Definitions

• Probability the measure of the likely hood of
  an event.
• Event a desired outcome of an experiment.
• Outcome a result from an experiment.
• Sample Space Collection of all possible
  outcomes
• Equation P(E)

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Probability Cont

• All answers for probability questions
• 0 lt P(E) lt 1
• Thus all answers are written as fractions,
  decimals or percents, or 1 or Zero!
• Certain Events 1 or 100
• Impossible Events ZERO.

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Classic Probability Experiments
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Roll of a die 1,2,3,4,5,6

• P(1)
• P(even)
• P(7)
• P(prime)

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Bag o marbles 2 blue,3 red,5 white,1 yellow

• 1) P(red)
• P(red or blue)
• P(green)
• Total of all probabilities 1 (or 100)

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Deck of playing cards52 cards, 4 suits, red
and black

• P(4 of diamonds)
• P(club)
• P(queen)
• P(face card)

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Compound Events

• Involves two or more experiments at the same
  time.
• Ex. (1) Rolling two dice together

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Compound Events cont

• To find the total number of possibilities of more
  than one event, simply multiply the total number
  of possibilities of each.
• This is called the Counting principle
• Ex (1) Flipping 2 coins 4, because each has two
  poss.
• Ex (2) The roll of a die and flip of a coin 12
• Ex (3) Selecting a outfit from 3 different
  shirts, 2 pairs of slacks, 5 ties 3x2x5 30

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Tree Diagram

• Tree diagrams are a visual outline (flow chart)
  of each possible event.
• When completed the will list all the possible
  outcomes of a Sample space.
• Ex Flip of a coin and roll of a die

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With or Without Replacement

• Replacing simply means to place the object back
  into the total possibilities before re-drawing
• Without replacement means to keep the desired
  object out from the total.
• To find the probability of more than one event,
  Multiply their probabilities.

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Deck of playing cards (without replacement)52
cards, 4 suits, red and black

• P(4 of diamonds and a 5 of clubs)
• P(two clubs)
• P(Ace and a King)
• P(four aces)

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Flipping coins

• Ex (1) What is the probability of getting Tails 3
  times in a row?
• Ex (2) If we received tails 5 times in a row,
  what is the probability it will be tails on the
  6th toss?
• Ex (3) What is the probability of getting heads 6
  times in a row?

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Having kids?

• Ex (1) If you were to have 4 children, what is
  the probability of having 4 boys?
• Make a tree diagram to display the sample space.

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How many ways?

• Ex (2) At NCCC, there are 10 doors that can be
  used to enter the building and 2 stairways to the
  Library. How many different routes are there from
  outside the building to the Library, and then
  back out of the building?

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Sandwich Shop

• Ex (3) A sandwich shop in town has Plain, Wheat
  and Italian rolls, 5 types of meat, 3 cheeses,
  and 4 toppings to choose from.
• How many different sandwiches can be created with
  with one of each?
• How many sandwiches can be created with a roll,
  two different meats, and cheese?
• What is the probability of selecting a sandwich
  with a wheat roll?