Sample Space

1
Sample Space

• A theater uses a letter to show which row a seat
  is in, and a number to show the column the seat
  is in. If there are rows A-J and numbers 1-20,
  how many seats are in the theater?
• 200 seats
• How does this relate to sample space in
  probability?

2
Sample Space is the set of all possible outcomes
of a situation

• If the theater has A-J rows and 1-20 seats, what
  is the probability you sit in any seat in row D?
• Probability of sitting in row D or E?

3
In Probability

• Number of favorable outcomes
• Number of possible outcomes
• P(choosing red marble from bag of 5 yellow, 3
  black and 4 red)
• 4/12 1/3
• P(rolling 7 on 2 number cubes)
• 6,15,22,53,44,31,6 6/36 1/6
• P(flipping coin twice and getting 2 heads)
• ½ ½ ¼
• Why do you add versus multiply in probability?

4

• Susan, Joanne, and Dianne are triplets. Susan
  has red, blue, green and yellow sweaters. Joanne
  has green, red, purple and white sweaters.
  Dianne has red, blue, purple, and mauve. They
  pick sweaters to wear at random.
• List all the possible outcomes first.
• P(each girl chooses different color)
• 21/32
• P(each girl chooses same color)
• 1/64
• P( two girls choose same color, and third chooses
  different color)
• 21/64
• P(each girl chooses a red sweater)
• 1/64

5
Theoretical Probability what theoretically
should happen

• A letter is selected at random from letters of
  FLORIDA. What is probability the letter is an A?
• 7 letters to choose from (possible outcomes)
• 1 A possible (favorable outcome)
• 1/7
• Complement of event A (not A)?
• 7 to choose from (possible outcomes)
• 6 not As
• 6/7
• Probabilities of an event and its complement add
  to 1 or 100

6
Theoretical Probability

• Use the letters MATHEMATICS. Find each
  probability.
• 1) P(M)
• 2/11
• 2) P(not vowel)
• 7/11
• P(not E)
• 10/11
• P(T or S)
• 2/11 1/11 3/11