Introductory Statistics
Lesson 3.2 A
Objective: SSBAT find conditional probability.
Standards: M11.E.3.1.1
Conditional Probability
 The probability of an event occurring, given that
another event has already occurred.
 Notation:
P(B│A) means Probability of event B occurring
given event A has occurred
P(A│B) means Probability of event A occurring
given event B has occurred
Examples.
1. Two cards are selected in sequence from a deck
of cards. Find the probability that he second card
is a queen, given that the first card is a king. The
king is not replaced.
 Since the first card was a King and it was not
replaced, there are now just 51 cards
remaining, with 4 queens.
P(Q│K) =
4
51
or 0.078
2. Two cards are chosen in sequence from a deck of
cards. Find the probability that the second card is a
heart, given the first card was the 10 of hearts. The
first card is not replaced.
 After the first card is chosen, there are just 51
cards remaining. The first card was also a
heart, so now there are just 12 hearts.
P(Heart│10 of Hearts) =
12
51
or 0.235
3. The table shows the results of a study in which researchers
examined a child’s IQ and the presence of a specific gene in
the child. Find the probability that a child has a high IQ, given
Gene
Gene
Total
that the child has the gene.
Find the Probability that a child
has a high IQ, given that the
child has the gene.
Present
not
present
High IQ
33
19
52
Normal
IQ
39
11
50
Total
72
30
102
 Since we know the child has the gene, we can just look at
this column. There are 72 total children in this category.
 Using just this category, find the Probability of High IQ.
33
P(High IQ │Gene Present) =
72
=
11
24
or 0.458
4. Use the same table to find the Probability that a child does
not have the gene, given that the child has a normal IQ.
 We are given the child has a
Normal IQ, so therefore we will
just use this data (row).
 There are a total of 50 children
who have a normal IQ.
P(No Gene│Normal IQ) =
𝟏𝟏
𝟓𝟎
Gene
Present
Gene
not
present
Total
High IQ
33
19
52
Normal
IQ
39
11
50
Total
72
30
102
or 0.22
Independent Events
 Two events are Independent if the occurrence of
one of the events does NOT affect the probability of
the other event.
 Example - Rolling a Die and Tossing a Coin
What you roll on the die does not affect what
you toss on the coin.
 If events are not independent they are Dependent
Examples: Determine if the events are Independent or Dependent
1. Selecting a King from a deck of cards, not replacing it, and
then selecting a Queen from the deck.

Dependent (not replacing the king changes the
probability of selecting a queen)
2. Tossing a coin and getting a head, and then rolling a die
and getting a 6.

Independent
(what you get on the coin does
not affect what you get on the die)
3. Driving 80 miles per hour and then getting a speeding
ticket.

Dependent
4. Smoking a pack of cigarettes per day and developing
emphysema (a lung disease)

Dependent
5. Exercising frequently and having a 4.0 grade point average

Independent
Complete worksheet 3.2 A