Conditional Probability
Engr. Maria Romina P. Angustia
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:
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
• "Probability of event A and event B equals
the probability of event A times the
probability of event B given event A"
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
Deriving the formula for Conditional
Probability:
Note: This expression
is only valid
when P(A) is greater
than 0.
• "The probability of event B given event
A equals the probability of event A and event
B divided by the probability of event A.”
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%