1. Name ___________________________________ Date ______________________
Mrs. Labuski & Mrs. Rooney Period _______ Lesson 11-5B Independent &
Dependent Events
VOCABULARY DEFINITION EXAMPLE
Pick One Pick Two
INDEPENDENT
EVENTS
Pick One Pick Two
DEPENDENT
EVENTS
Determine whether the following events are independent or dependent.
1. Kathy draws a 4 from a set of cards
numbered 1-10 and rolls a 2 on a number cube. ___________________
2. John chooses a book from the shelf to read, and then
Brian chooses a different book from the remaining books. ___________________
3. Adrian chooses a baseball card from a stack and does
not return it to the stack. Then Jenna chooses a card from stack. _______________
4. Mike draws a 7 from ten cards numbered
1 through 10. He replaces the card. Then Allison draws a 5. _________________

2. To find the probability of Two Independent Events:
P(A and B) = P(A) • P(B)
probability probability probability
of both events of first event of second event
Find the probability of rolling a 3 on a die & the spinner shown landing on A.
P(3 and A) = P(3) • P(A)
P(3 and A) =
P(3 and A) =
The probability of rolling a 3 and the spinner landing on A is _________________.
Now you try: Find the probability of each event for the spinners shown.
1. The spinners land on 1 and E. 2. The spinners land on even number and A.
P(1 and E) P(even number and A
3. The spinners land on an odd number and A, B, C, or D.
P(odd number and A,B,C,D)

3. To find the probability of Two Dependent Events:
P(A and B) = P(A) • P(B after A)
probability probability probability of second event
of both events of first event after the first event has occurred
A bag contains 2 black marbles and 3 white marbles.
Find the probability of drawing a black marble and putting
it aside and then a drawing a white marble.
P(black and white) = P(black) • P(white after black)
P(black and white) =
P(black and white) =
The probability of drawing a black marble and then a white marble is ___________.
Now you try: Find the probability of each event when after the first draw you do
not return the marble to the bag.
1. P(white and black) _____________ 2. P(2 white marbles) _____________
Nicole has 10 coins in her purse: 3 pennies, 3 nickels, 2 dimes, and 2 quarters.
Nicole draws one coin from her purse and puts it on the counter.
3. What is the probability that Nicole 4. What is the probability that Nicole
will draw a penny and a dime? will draw a quarter and a nickel?

4. Name ___________________________________ Date ______________________
Mrs. Labuski & Mrs. RooneyPeriod _______ Lesson 11-5B Independent &
Dependent Events
VOCABULARY DEFINITION EXAMPLE
Pick One Pick Two
The occurrence of
one event has no
INDEPENDENT effect on the
EVENTS probability that the
second event will You pick a marble from the
bag and then you put it back
occur. before the second pick.
Pick One Pick Two
The occurrence of
one event has an
DEPENDENT effect on the
EVENTS probability that the
second event will You pick a marble from the
bag and then you do not put it
occur. back before the second pick.
Determine whether the following events are independent or dependent.
1. Kathy draws a 4 from a set of cards
numbered 1-10 and rolls a 2 on a number cube. independent
2. John chooses a book from the shelf to read, and then
Brian chooses a different book from the remaining books. dependent
3. Adrian chooses a baseball card from a stack and does
not return it to the stack. Then Jenna chooses a card from stack. dependent
4. Mike draws a 7 from ten cards numbered
1 through 10. He replaces the card. Then Allison draws a 5. independent

5. To find the probability of Two Independent Events:
P(A and B) = P(A) • P(B)
probability probability probability
of both events of first event of second event
Find the probability of rolling a 3 on a die & the spinner shown landing on A.
P(3 and A) = P(3) • P(A)
1 • 1
P(3 and A) = 6 5
1
P(3 and A) = 30
1
The probability of rolling a 3 and the spinner landing on A is ____30___________.
Now you try: Find the probability of each event for the spinners shown.
1. The spinners land on 1 and E. 2. The spinners land on even number and A.
P(1 and E) P(even number and A)=
1 • 1 = 1 3 • 0 = 0
4 5 20 6
3. The spinners land on an odd number and A, B, C, or D.
P(odd number and A,B,C,D)
2• 4= 8 =4
4 5 20 5
(You can cross reduce before multiplying!)

6. To find the probability of Two Dependent Events:
P(A and B) = P(A) • P(B after A)
probability probability probability of second event
of both events of first event after the first event has occurred
A bag contains 2 black marbles and 3 white marbles.
Find the probability of drawing a black marble and putting
it aside and then a drawing a white marble.
P(black and white) = P(black) • P(white after black)
2 • 3
P(black and white) = 5 4
P(black and white) = 6 = 3
20 10 3
The probability of drawing a black marble and then a white marble is __10______.
Now you try: Find the probability of each event when after the first draw you do
not return the marble to the bag.
1. P(white and black) _____________ 2. P(2 white marbles) _____________
3• 2= 6 =3 3• 2= 6 =3
5 4 20 10 5 4 20 10
(You can cross reduce before multiplying!)
Nicole has 10 coins in her purse: 3 pennies, 3 nickels, 2 dimes, and 2 quarters.
Nicole draws one coin from her purse and puts it on the counter.
3. What is the probability that Nicole 4. What is the probability that Nicole
will draw a penny and a dime? will draw a quarter and a nickel?
P(penny and dime) = P(quarter and nickel) =
3• 2= 6 = 1 2• 3= 6 = 1
10 9 90 15 10 9 90 15