Sec' 12'7 Conditional Probability

1
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
2
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
3
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
ex. A single die is rolled. Find the
probability of rolling a 2 given that
the number is even
4
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
ex. A single die is rolled. Find the
probability of rolling a 2 given that
the number is even
5
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
ex. A single die is rolled. Find the
probability of rolling a. a 6 given
that the number is even b. a number
less than 3 given the number is less than 5
6
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
ex. A single die is rolled. Find the
probability of rolling a. a 6 given
that the number is even b. a number
less than 3 given the number is less than 5
7
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
ex. A single die is rolled. Find the
probability of rolling a. a 6 given
that the number is even b. a number
less than 3 given the number is less than 5
8
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
ex. A single die is rolled. Find the
probability of rolling a. a 6 given
that the number is even b. a number
less than 3 given the number is less than 5
9
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
ex. Given a family with two children, and
assuming that boys and girls are equally
likely, find the probability than the family has
a. two girls b. two
girls if you know at least one of the children is
a girl c. two girls given that the
older child is a girl d. no girls
e. at least one girl
10
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
Sample space
ex. Given a family with two children, and
assuming that boys and girls are equally
likely, find the probability than the family has
a. two girls b. two
girls if you know at least one of the children is
a girl c. two girls given that the
older child is a girl d. no girls
e. at least one girl
11
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
Sample space BB, BG, GB, GG
ex. Given a family with two children, and
assuming that boys and girls are equally
likely, find the probability than the family has
a. two girls b. two
girls if you know at least one of the children is
a girl c. two girls given that the
older child is a girl d. no girls
e. at least one girl
12
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
Sample space BB, BG, GB, GG
ex. Given a family with two children, and
assuming that boys and girls are equally
likely, find the probability than the family has
a. two girls b. two
girls if you know at least one of the children is
a girl c. two girls given that the
older child is a girl d. no girls
e. at least one girl
13
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
Sample space BB, BG, GB, GG
ex. Given a family with two children, and
assuming that boys and girls are equally
likely, find the probability than the family has
a. two girls b. two
girls if you know at least one of the children is
a girl c. two girls given that the
older child is a girl d. no girls
e. at least one girl
14
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
Sample space BB, BG, GB, GG
ex. Given a family with two children, and
assuming that boys and girls are equally
likely, find the probability than the family has
a. two girls b. two
girls if you know at least one of the children is
a girl c. two girls given that the
older child is a girl d. no girls
e. at least one girl
15
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
Sample space BB, BG, GB, GG
ex. Given a family with two children, and
assuming that boys and girls are equally
likely, find the probability than the family has
a. two girls b. two
girls if you know at least one of the children is
a girl c. two girls given that the
older child is a girl d. no girls
e. at least one girl
16
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
Sample space BB, BG, GB, GG
ex. Given a family with two children, and
assuming that boys and girls are equally
likely, find the probability than the family has
a. two girls b. two
girls if you know at least one of the children is
a girl c. two girls given that the
older child is a girl d. no girls
e. at least one girl
17
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
Sample space BB, BG, GB, GG
ex. Given a family with two children, and
assuming that boys and girls are equally
likely, find the probability than the family has
a. two girls b. two
girls if you know at least one of the children is
a girl c. two girls given that the
older child is a girl d. no girls
e. at least one girl
18
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
Sample space BB, BG, GB, GG
ex. Given a family with two children, and
assuming that boys and girls are equally
likely, find the probability than the family has
a. two girls b. two
girls if you know at least one of the children is
a girl c. two girls given that the
older child is a girl d. no girls
e. at least one girl
19
Sec. 12.7 Conditional Probability
Def The probability of event E2 occurring,
given that E1 has occurred is called a
conditional probability and is written P(E2/E1).
P(E2/E1)
Sample space BB, BG, GB, GG
ex. Given a family with two children, and
assuming that boys and girls are equally
likely, find the probability than the family has
a. two girls b. two
girls if you know at least one of the children is
a girl c. two girls given that the
older child is a girl d. no girls
e. at least one girl