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12.3 – Conditional Probability
• Given that A and B are dependent events, the
conditional probability of an event B, given
that event A has already occurred, is
P(B|A) = P(A and B)
P(A)
• Given that A and B are dependent events, the
conditional probability of an event B, given
that event A has already occurred, is
P(B|A) = P(A and B)
P(A)
Ex. 1 If a die is rolled, what is the probability
that a 3 was rolled given that the number is odd
• Given that A and B are dependent events, the
conditional probability of an event B, given
that event A has already occurred, is
P(B|A) = P(A and B)
P(A)
Ex. 1 If a die is rolled, what is the probability
that a 3 was rolled given that the number is odd
P(3|odd)
• Given that A and B are dependent events, the
conditional probability of an event B, given
that event A has already occurred, is
P(B|A) = P(A and B)
P(A)
Ex. 1 If a die is rolled, what is the probability
that a 3 was rolled given that the number is odd
P(3|odd) = P(odd and 3)
• Given that A and B are dependent events, the
conditional probability of an event B, given
that event A has already occurred, is
P(B|A) = P(A and B)
P(A)
Ex. 1 If a die is rolled, what is the probability
that a 3 was rolled given that the number is odd
P(3|odd) = P(odd and 3)
P(odd)
• Given that A and B are dependent events, the
conditional probability of an event B, given
that event A has already occurred, is
P(B|A) = P(A and B)
P(A)
Ex. 1 If a die is rolled, what is the probability
that a 3 was rolled given that the number is odd
P(3|odd) = P(odd and 3)
P(odd)
• Given that A and B are dependent events, the
conditional probability of an event B, given
that event A has already occurred, is
P(B|A) = P(A and B)
P(A)
Ex. 1 If a die is rolled, what is the probability
that a 3 was rolled given that the number is odd
P(3|odd) = P(odd and 3)
P(odd)
= 1/6
• Given that A and B are dependent events, the
conditional probability of an event B, given that
event A has already occurred, is
P(B|A) = P(A and B)
P(A)
Ex. 1 If a die is rolled, what is the probability that a
3 was rolled given that the number is odd
P(3|odd) = P(odd and 3)
P(odd)
= 1/ 6
1/
2
• Given that A and B are dependent events, the
conditional probability of an event B, given that
event A has already occurred, is
P(B|A) = P(A and B)
P(A)
Ex. 1 If a die is rolled, what is the probability that a
3 was rolled given that the number is odd
P(3|odd) = P(odd and 3)
P(odd)
= 1/ 6 = 1/ 3
1/
2
Ex. 2 Find the probability that a test subject
stayed healthy, given that he or she used an
experimental drug.
Condition
Sick (S)
Healthy (H)
Number of Subjects
Using Drug (D) Using Placebo (P)
1600
1200
800
400
Ex. 2 Find the probability that a test subject
stayed healthy, given that he or she used an
experimental drug.
Condition
Sick (S)
Healthy (H)
Total = 4000
Number of Subjects
Using Drug (D) Using Placebo (P)
1600
1200
800
400
Ex. 2 Find the probability that a test subject
stayed healthy, given that he or she used an
experimental drug.
Condition
Sick (S)
Healthy (H)
Number of Subjects
Using Drug (D) Using Placebo (P)
1600
1200
800
400
Total = 4000
P(H|D)
Ex. 2 Find the probability that a test subject
stayed healthy, given that he or she used an
experimental drug.
Condition
Sick (S)
Healthy (H)
Number of Subjects
Using Drug (D) Using Placebo (P)
1600
1200
800
400
Total = 4000
P(H|D) = P(H and D)
Ex. 2 Find the probability that a test subject
stayed healthy, given that he or she used an
experimental drug.
Condition
Sick (S)
Healthy (H)
Number of Subjects
Using Drug (D) Using Placebo (P)
1600
1200
800
400
Total = 4000
P(H|D) = P(H and D)
P(D)
Ex. 2 Find the probability that a test subject
stayed healthy, given that he or she used an
experimental drug.
Condition
Sick (S)
Healthy (H)
Number of Subjects
Using Drug (D) Using Placebo (P)
1600
1200
800
400
Total = 4000
P(H|D) = P(H and D)
P(D)
= 800/4000
Ex. 2 Find the probability that a test subject
stayed healthy, given that he or she used an
experimental drug.
Condition
Sick (S)
Healthy (H)
Number of Subjects
Using Drug (D) Using Placebo (P)
1600
1200
800
400
Total = 4000
P(H|D) = P(H and D)
P(D)
= 800/4000
2400/
4000
Ex. 2 Find the probability that a test subject
stayed healthy, given that he or she used an
experimental drug.
Condition
Sick (S)
Healthy (H)
Number of Subjects
Using Drug (D) Using Placebo (P)
1600
1200
800
400
Total = 4000
P(H|D) = P(H and D)
P(D)
= 800/4000 = 800/2400
2400/
4000
Ex. 2 Find the probability that a test subject
stayed healthy, given that he or she used an
experimental drug.
Condition
Sick (S)
Healthy (H)
Number of Subjects
Using Drug (D) Using Placebo (P)
1600
1200
800
400
Total = 4000
P(H|D) = P(H and D)
P(D)
= 800/4000 = 800/2400 = 1/3
2400/
4000
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