Conditional ProbabilityEngr. 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) =

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%