Lesson 25: Intro to Probability

1
Lesson 25 Intro to Probability

• Objectives
• Name the two definitions of probability
• Determine the probability of an event which is a
  subset of equally likely outcomes
• Determine the probability of drawing two red
  balls (without replacement) from an urn with 3
  red balls and 4 green balls

• Outline
• Review of Chapter 4
• Definition of Probability
• Examples of Probability

2
Description of Probability

• Repeated Events
• Success vs. Failure

3
Laplaces Definition of Probability

• Experiment a procedure that yields an outcome
• Sample Space Set of possibilities
• Event Subset of Sample Space
• Probability of an event E, p(E) E/S

4
Laplaces Definition

• What is the probability of drawing a spade from a
  deck of regular playing cards?

5
Lottery

• What is the probability of winning the
  PowerBall, where the numbers are from 1-60, and
  you must match 6 numbers to win (in any order)?

6
Cards

• How many different hands can be dealt from a
  standard deck?

7
Passwords

• A password consists of five lowercase letters,
  where each letter has an equal chance of being
  chosen
• Find the probability that the password begins
  with c
• Find the probability that there are no vowels in
  the password

8
True/False

• A true/false quiz has 10 questions. If you
  randomly answer each question, what is the
  probability that you score at least 70?

9
Lottery

• In a lottery game, a winning set of five numbers
  is chosen from the set 1,2,344 . To play, you
  pick a set of five numbers. If your five numbers
  match the five winning numbers, you win first
  prize. If exactly four match, you win second
  prize. If exactly three match, you win third
  prize. Otherwise you lose. Find
• (a) p(win first prize).
• (b) p(win second prize).
• (c) p(win third prize).
• (d) p(you lose).

10
PowerBall

• What is the probability that the numbers 11, 15,
  19, 18, and 45 are drawn in that order from the
  Powerball bin?
• The sequence 11, 15, 19, 11, 45?

11
Axioms of Probability

• The Probability of an event, p(E) is between 0
  and 1, inclusively.
• The probability of an event E not happening is
• 1 - p(E)
• - Ten bits are randomly generated. What is the
  probability that at least one of the bits is a 0?

12
Union of two events

• Let E1 and E2 be events in sample space S
• p(E1 ? E2) p(E1) p(E2) - p(E1 ? E2)
• What is the probability that a positive integer
  selected at random less than or equal to 1000 is
  divisible by either 2 or 5?