Download 2-7ProbabilityOfCompoundEvents

Chapter 2: Rational Numbers
2.7
Probability of Compound Events
Independent Events
• Events that do not influence each other
• Example:
– Drawing a card, then putting it back before drawing
another
• Probability of Two Independent Events:
– If A and B are independent events:
P( AandB)  P( A)  P( B)
Example 1
• Suppose you roll a red number cube and a blue
number cube. What is the probability that you will
roll a 3 on the red cube and an even number on the
blue cube?
Example 1a
• Suppose you roll a red number cube and a blue
number cube. What is the probability that you will
roll a 5 on the red cube and a 1 or 2 on the blue
cube?
Example 2
• In a word game, you choose a tile at random from a
bag containing the letter tiles I, U, I, A, O, O, O, E, A,
U, A, O, A, E, E. You replace the first tile in the bag
and then choose again. What is the probability that
you will choose an A and then an E?
Example 2a
• In a word game, you choose a tile at random from a
bag containing the letter tiles I, U, I, A, O, O, O, E, A,
U, A, O, A, E, E. Find the probability that you will
choose at random a U and then an I after replacing
the first tile.
Probability of Two Dependent Events
• Dependent events
– Events that influence each other
• Probability:
P( AthenB)  P( A)  P( BafterA)
Example 3
• Suppose you choose a tile at random from the letter
tiles I, U, I, A, O, O, O, E, A, U, A, O, A, E, E. Without
replacing the tile, you select a second tile. What is
the probability that you will choose an A and then
an E?
Example 3a
• Suppose you choose a tile at random from the letter
tiles I, U, I, A, O, O, O, E, A, U, A, O, A, E, E. Find the
probability that you will choose at random a U and
then an O without replacing the first tile.
Example 4
• Suppose a teacher must select 2 high school
students to represent their school at a conference.
The teacher randomly picks names from a hat that
contains the names of 3 freshmen, 2 sophomores, 4
juniors, and 4 seniors. What is the probability that
a sophomore and then a freshman are chosen?
Example 4a
• Suppose a teacher must select 2 high school
students to represent their school at a conference.
The teacher randomly picks names from a hat that
contains the names of 3 freshmen, 2 sophomores, 4
juniors, and 4 seniors. What is the probability that
a sophomore and then a junior are chosen?
Example 4b
• Suppose a teacher must select 2 high school
students to represent their school at a conference.
The teacher randomly picks names from a hat that
contains the names of 3 freshmen, 2 sophomores, 4
juniors, and 4 seniors. What is the probability that
a junior and then a sophomore are chosen?
Homework
• P. 104
• 2-28 even, 36-40 even