Algebra 2

1
11-2Probability

• Algebra 2
• Mr. Gallo

2
Terms to Know

• Probability is the ratio of the number of
  _______________________ to the ___________ number
  of possible outcomes.
• Probability

total
favorable outcomes
3
Rules

• Probability is expressed as a ______________,
  ____________, or _____________ with a value
  greater than or equal to _______________ and less
  than or equal to ___________.
• (0 ? P ? 1)
• If P(A) 0, then this represents an
  ___________________.
• If P(A) 1, then this represents a
  ____________________.

fraction
decimal
percent
zero
one
impossible event
certain event
4
Experimental Probability

• Experimental probability A calculation of the
  probability of an event based on
  _______________________,
• ____________________ or looking at the history
  of an event.

performing an experiment
conducting a survey
You observe 119 animals at a zoo, 19 of them have
wings. What is the experimental probability that
an animal at this zoo has wings?
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Example 1

• The first exam grades of students in a biology
  class are shown in the bar graph. Find the
  probability that a randomly chosen student in
  this biology class received a B or better.

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Simulations

• Can be used in place of expensive studies.
• Used by John von Neuman and Stanislaw Ulam for
  behavior of neutrons during atomic bomb
  development.
• Uses random numbers, die, coins, etc. to simulate
  situations and generate experimental
  probabilities.

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Example 2

• On a multiple choice test, each item has three
  choices, but only one choice is correct. How can
  you simulate guessing the answers? What is the
  probability that you will pass the test by
  guessing at least five of ten answers correctly?

1. Use integers 1, 2, 3 to represent the three
   answer choices.
2. Assign 1 to represent the correct answer and 1
   3 to represent the incorrect answers.
3. Use RANDINT( Lowest integer, Highest Integer,
   Number of outcomes). In the calculator type
   randint(1,3,10) to represent the answers for the
   10 questions.
4. Repeat the simulation at least 20 times, keeping
   track of results.
5. Use results to calculate experimental
   probability. Should be approximately 21.3.

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Homework p. 685 8-12, 42-45
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Theoretical Probability

• is the number of outcomes divided by the total
  number of outcomes and is often referred to as
  the ___________________ of an event.

probability
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Example 3

• A standard die is rolled. Find each of the
  following
• a. The probability of rolling a 5.
• b. The probability of rolling an even number.
• c. The probability of rolling a number less
  than 3.
• d. The probability of rolling a number greater
  than 7.
• e. The probability of rolling a number less than
  7.

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Example 4

• A card is randomly selected from a deck of cards.
  What is the probability of selecting a queen or
  a jack?

4 Jack in a deck
4 Queens in a deck
52 cards in a standard deck.
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Geometric probability

• Geometric probability A type of probability
• found by calculating a ___________________,
• ____________, or ___________________.

ratio of two lengths
areas
volumes
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Example 5

• You throw a ball into a square basket. What is
  the probability that it lands inside the circle?
  Assume that the ball is equally likely to hit any
  point inside the basket.

r2
W5
L9
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Homework p. 685 13-21 odd, 24-26, 29-32