Conditional probability is the probability of an event occurring given that another event has occurred. It is calculated as the probability of both events occurring divided by the probability of the first event. An example is given of calculating the probability of drawing two white balls in succession from an urn without replacement. The formula for conditional probability is derived as the probability of events A and B occurring divided by the probability of A. This is demonstrated using an example of finding the percentage of friends who like chocolate that also like strawberry.

1. Conditional Probability
Engr. Maria Romina P. Angustia

2. Conditional Probability:
• the probability of an event ( A ), given that
another ( B ) has already occurred.
• Where two events, A and B, are dependent.
• The probability of both occurring is:

3. Where:
• P(A) -the probability of event A may
happen
• P(B) -the probability of event B may
happen
• P(A/B) –the probability of event B
given/without A

4. • "Probability of event A and event B equals
the probability of event A times the
probability of event B given event A"

5. Example:
• An urn contains 3 white balls and 1 black ball.
Determine the probability of drawing two
white balls in succession from the urn without
replacing the ball after each drawing.
• P(A and B) =
3
4
𝑥
2
3
=
1
2

6. Deriving the formula for Conditional
Probability:
Note: This expression
is only valid
when P(A) is greater
than 0.

7. • "The probability of event B given event
A equals the probability of event A and event
B divided by the probability of event A.”

8. Example:
• 70% of your friends like Chocolate, and 35%
like Chocolate AND like Strawberry. What
percent of those who like Chocolate also like
Strawberry?
• P(Strawberry|Chocolate) = P(Chocolate and
Strawberry) / P(Chocolate)
P(Strawberry|Chocolate) =0.35 / 0.7 = 50%