PPT - Conditional probability

# PPT - Conditional probability - Business Mathematics and Statistics - B Com

``` Page 1

Probability
Conditional Probability
Page 2

Probability
Conditional Probability
Conditional Probability
? When we want the probability of an event from a
conditional distribution, we write P(B|A) and
pronounce it “the probability of B given A.”
? A probability that takes into account a given
condition is called a conditional probability.
Page 3

Probability
Conditional Probability
Conditional Probability
? When we want the probability of an event from a
conditional distribution, we write P(B|A) and
pronounce it “the probability of B given A.”
? A probability that takes into account a given
condition is called a conditional probability.
Conditional Probability (cont.)
? To find the probability of the event B given the
event A, we restrict our attention to the outcomes
in A. We then find in what fraction of those
outcomes B also occurred.
? Note: P(A) cannot equal 0, since we know that A
has occurred.
(A and B)
( | )
()
P
P
P
? BA
A
Page 4

Probability
Conditional Probability
Conditional Probability
? When we want the probability of an event from a
conditional distribution, we write P(B|A) and
pronounce it “the probability of B given A.”
? A probability that takes into account a given
condition is called a conditional probability.
Conditional Probability (cont.)
? To find the probability of the event B given the
event A, we restrict our attention to the outcomes
in A. We then find in what fraction of those
outcomes B also occurred.
? Note: P(A) cannot equal 0, since we know that A
has occurred.
(A and B)
( | )
()
P
P
P
? BA
A
Independence
? Independence of two events means that the
outcome of one event does not influence the
probability of the other.
? With our new notation for conditional
probabilities, we can now formalize this definition:
? Events A and B are independent whenever
P(B|A) = P(B). (Equivalently, events A and B
are independent whenever P(A|B) = P(A).)
Page 5

Probability
Conditional Probability
Conditional Probability
? When we want the probability of an event from a
conditional distribution, we write P(B|A) and
pronounce it “the probability of B given A.”
? A probability that takes into account a given
condition is called a conditional probability.
Conditional Probability (cont.)
? To find the probability of the event B given the
event A, we restrict our attention to the outcomes
in A. We then find in what fraction of those
outcomes B also occurred.
? Note: P(A) cannot equal 0, since we know that A
has occurred.
(A and B)
( | )
()
P
P
P
? BA
A
Independence
? Independence of two events means that the
outcome of one event does not influence the
probability of the other.
? With our new notation for conditional
probabilities, we can now formalize this definition:
? Events A and B are independent whenever
P(B|A) = P(B). (Equivalently, events A and B
are independent whenever P(A|B) = P(A).)
The General Multiplication Rule
? When two events A and B are independent, we
can use the multiplication rule for independent
events :
P(A and B) = P(A) x P(B)
? However, when our events are not independent,
this earlier multiplication rule does not work.
Thus, we need the General Multiplication Rule.
```

115 videos|142 docs

## FAQs on PPT - Conditional probability - Business Mathematics and Statistics - B Com

 1. What is conditional probability?
Ans. Conditional probability is a measure of the probability of an event occurring given that another event has already occurred. It calculates the likelihood of an outcome based on additional information or conditions.
 2. How is conditional probability calculated?
Ans. Conditional probability is calculated by dividing the probability of the intersection of two events by the probability of the given condition. In mathematical terms, it is represented as P(A|B) = P(A ∩ B) / P(B), where A and B are two events.
 3. Can you provide an example of conditional probability?
Ans. Sure! Let's say you want to find the probability of drawing two black cards from a standard deck of playing cards, given that the first card drawn was a black card. The conditional probability can be calculated by dividing the number of favorable outcomes (26 black cards remaining) by the number of possible outcomes (51 cards remaining).
 4. How is conditional probability useful in real life?
Ans. Conditional probability has various applications in real life. It is used in weather forecasting to calculate the probability of rain given certain atmospheric conditions. It is also used in medical diagnosis, where the probability of a disease is determined based on various symptoms and test results.
 5. What is the difference between conditional probability and joint probability?
Ans. Conditional probability focuses on the probability of an event occurring given that another event has already occurred. On the other hand, joint probability deals with the probability of two or more events occurring simultaneously. Conditional probability is calculated using the joint probability and the probability of the given condition.

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