Transcript Dependent Events

Main Idea and Vocabulary
Example 1: Independent Events
Key Concept: Probability of Independent Events
Example 2: Real-World Example
Key Concept: Probability of Dependent Events
Example 3: Dependent Events
Example 4: Disjoint Events
Key Concept: Probability of Disjoint Events
• Find the probability of independent and
dependent events.
• compound event
• independent events
• dependent events
• disjoint events
Independent Events
The spinner to the right is spun and
a number cube is tossed. Find the
probability of spinning a C and
rolling a number less than 5.
List the sample space.
A, 1
A, 2
A, 3
A, 4
A, 5
A, 6
B, 1
B, 2
B, 3
B, 4
B, 5
B, 6
C, 1
C, 2
C, 3
C, 4
C, 5
C, 6
Independent Events
P
P
A coin is tossed and a number cube is rolled. Find
the probability of tossing heads and rolling an even
number.
A.
B.
C.
D.
LUNCH For lunch, Jessica may choose a turkey
sandwich, a tuna sandwich, a salad, or a soup. For
a drink, she can choose juice, milk, or water. If she
chooses a lunch and a drink at random, what is the
probability that she chooses a sandwich and juice?
Answer: The probability that she chooses a sandwich
and juice is
CLOTHES Zachary has a blue, a red, a gray, and a
white sweatshirt. He also has blue, red, and gray
sweatpants. If Zachary randomly pulls a sweatshirt
and a pair of sweatpants from his drawer, what is
the probability that they will both be blue?
A.
B.
C.
D.
Dependent Events
SOCKS There are 4 black, 6 white, and 2 blue
socks in a drawer. José randomly selects two
socks without replacing the first sock. What is the
probability that he selects two white socks?
Since the first sock is not replaced, the first event affects
the second event. These are dependent events.
number of white socks
total number of socks
number of white socks
after one is removed
total number of socks
after one is removed
Dependent Events
1
2
Answer: So, the probability of selecting two white socks
is
or about 22.7%.
GAMES Janet has a card game that uses a deck of
48 cards—16 red, 16 blue, and 16 green. If she
randomly selects two cards without replacing the
first, what is the probability that both are green?
A.
B.
C.
D.
Disjoint Events
MONTHS A month of the year is randomly selected.
What is the probability of the month ending in the
letter Y or the letter R?
These are disjoint events since it is impossible to have a
month ending in both the letter Y and the letter R.
There are 8 favorable outcomes:
January, February, May, July,
September, October, November,
or December.
There are 12 possible outcomes.
Answer: So, the probability of a month ending in the
letter Y or R is
.
MARBLES There are 12 yellow, 3 black, 5 red, and
8 blue marbles in a bag. Joseph randomly selects
one marble from the bag. What is the probability that
the marble selected will be black or red?
A.
B.
C.
D.