Math
Independent and Dependent
Events
What Are You Learning?

I CAN find the probability of
independent events.

I CAN find the probability of
dependent events.
Why Do You Need To Know
This?

Independent and
Dependent Events are
useful because it allows
you to find the probability
of multiple events.
Example 1


You have 4 cards with an M
written on them, 2 with an A, 6
with a T, and 8 with an H.
You draw an M
card at random
and replace it.
What is the
probability that the
next card you draw
at random will also
be an M card?
P(M)
2nd card
matches
P(M)
P(A)
P(A)
P(T)
P(T)
P(H)
P(H)
First Card
Example 2


You have 4 cards with an M
written on them, 2 with an A, 6
with a T, and 8 with an H.
You draw an M card
at random and do
not replace it. What
is the probability that
the next card you
draw at random will
also be an M card?
First Card
2nd card
matches
P(M)
P(M)
P(A)
P(A)
P(T)
P(T)
P(H)
P(H)
Do You Know?

For any letter, why is the probability for
selecting the second card with
replacement of first card different from
the probability of selecting the second
card without replacement of the first
card?
Vocabulary

Independent Event—
events in which the first
event does not affect the
second event.

Dependent Event—events
in which the first event
does affect the second
event.

The probability of two
independent events can be
found by multiplying the
probability of the first event
by the probability of the
second event.

The probability of two
dependent events is the
probability of the first event
times the probability that
the second event occurs
after the first.

P(A and B) = P(A) · P(B)

P(A and B) = P(A) · P(B
following A)
Independent Event Notes

Find the probability of each event and
multiply the two fractions!

You roll a # cube once. Then you roll it
again.

What is the probability that you get 2
on the first roll and a number greater
than 4 on the second roll?

Suppose you spin a spinner
that is numbered 1-10, then
toss a # cube. What is the
probability that you will spin
and toss an even #?

You pick a marble from
a bag containing 1
green marble, 4 red
marbles, 2 yellow
marbles, and 3 black
marbles. You replace
the first marble and
select a second one.
Find each probability.
a.
P(red and yellow)
b.
P(black and black)
c.
P(red and black)
d.
P(yellow and
black)
3 girls and 2 boys volunteer to represent
their class at a school assembly.

Mrs. McCutchen
selects one name and
then another from a
bag containing the
students’ names.
a. Find P(girl and girl)
b. Find P(boy and girl)

Suppose the group
consisted of 3 boys
and 2 girls.

Find P(girl and girl).
Dependent Events Notes


Denominator changes in the second
fraction – ALWAYS!
Numerator changes in the second
fraction ONLY if you are finding the
probability of two things that are the
same. Example: P (black, then black)
A student has 5 blue socks and 4
black socks.

He selects one
a. P(blue and black)
sock at random.
Without replacing
b. P(black and blue)
the sock, he selects
a second sock at
c. P(black and black)
random.

Find each
probability.
d. P(blue and blue)
PREALGEBRA


You select a letter at
random from the word
above. Without replacing
the letter, you select a
second card.
a.
P(P and G)
b.
P(E and A)
c.
P(E and another vowel)
d.
P(G and R or A)
e.
P(P or E and A)
f.
P(consonant and vowel)
Find each probability.
You roll a # cube twice.

What is the
probability
that you roll
each of the
following
pairs of #s?
a.
6 and 5
b.
6 and 2 or 5
c.
6 and # less than 4
d.
1 and 1
e.
even # and 2 or 5
f.
even # and odd #

A standard deck of
playing cards
contains 52 cards
in four suits of 13
cards each. Two
suits are red and
two suits are black.
Two cards are
chosen from the
deck one after
another.
a. P(2 hearts)
b. P(red and black)
c. P(Ace and King)
Are the events independent or
dependent?
a. You select a card. Without putting the
card back, you select a second card.
b. You select a card. After putting it
back, you select a second card.
c. You roll a number cube. You roll it
again.
Class Work
Worksheet E-52
Worksheet E-53