Probability of Compound Events
12-8
Probability of
Compound Events
Compound Event:
Consists of two or
more events linked by the word
and
or
by the word
or
Mutually Exclusive Events:
When two
events have no outcomes in common
Overlapping Events:
When events
have at least one outcome in common
Problem 1: Mutually Exclusive and
Overlapping Events
Suppose you spin a spinner that has 20 equal-
sized sections numbered from 1 to 20.
•
What is the probability that you spin a 2 or a
5?
•
What is the probability that you spin a
number that is a multiple of 2 or 5?
Problem 2: Finding the Probability of
Independent Events
Suppose you roll a red number cube (dice)
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?
•
What is the probability that you roll a 5
on the red cube and a 1 or 2 on the blue
cube?
Problem 3: Selecting with Replacement
You choose a tile at random
from the game tiles shown.
You
replace the first tile
and then
choose again.
•
What is the probability that
you choose a dotted tile and
then a dragon tile?
You choose a tile at random
from the game tiles shown. You
replace the first tile and then
choose again.
•
What is the probability that
you choose a bird and then a
flower?
Problem 4: Selecting without Replacement
Suppose you choose a tile at
random from the tiles shown.
Without replacing
the first tile,
you select a second tile.
•
What is the probability that
you choose a dotted tile and
then a dragon tile?
Suppose you choose a tile at
random from the tiles shown.
Without replacing
the first tile,
you select a second tile.
•
What is the probability that
you choose a flower tile and
then a bird tile?
Learn about compound events in probability, including mutually exclusive events, overlapping events, and independent events. Explore formulas and solve problems related to spinning a spinner, rolling number cubes, and selecting tiles with and without replacement.
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Presentation Transcript
12-8 Probability of Compound Events
Compound Event: Consists of two or more events linked by the word and or by the word or Mutually Exclusive Events: When two events have no outcomes in common Overlapping Events: When events have at least one outcome in common
FORMULAS Mutually Exclusive Events: ? ? ?? ? = ? ? + ?(?) Overlapping Events: ? ? ?? ? = ? ? + ? ? ?(? ??? ?)
Problem 1: Mutually Exclusive and Overlapping Events Suppose you spin a spinner that has 20 equal- sized sections numbered from 1 to 20. What is the probability that you spin a 2 or a 5? What is the probability that you spin a number that is a multiple of 2 or 5?
Independent Events: if the occurrence of one event does not affect the probability of the second event. FORMULA ? ? ??? ? = ?(?) ?(?)
Problem 2: Finding the Probability of Independent Events Suppose you roll a red number cube (dice) 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? What is the probability that you roll a 5 on the red cube and a 1 or 2 on the blue cube?
Problem 3: Selecting with Replacement You choose a tile at random from the game tiles shown. You replace the first tile and then choose again. What is the probability that you choose a dotted tile and then a dragon tile?
You choose a tile at random from the game tiles shown. You replace the first tile and then choose again. What is the probability that you choose a bird and then a flower?
Dependent Events: If the occurrence of one event affects the probability of the second event. FORMULA ? ? ? ?? ? = ?(?) ?(? ????? ?)
Problem 4: Selecting without Replacement Suppose you choose a tile at random from the tiles shown. Without replacing the first tile, you select a second tile. What is the probability that you choose a dotted tile and then a dragon tile?
Suppose you choose a tile at random from the tiles shown. Without replacing the first tile, you select a second tile. What is the probability that you choose a flower tile and then a bird tile?
