1. Conditional Probability and Geometric Probability

2. Conditional Probability
P(A B) means “Probability that A occurs GIVEN that B has occurred. Formula P(A B) = P(A and B) P(B)

3. Example
Used Didn’t Drug Use Positive Test Negative Test What is the probability that someone tested positive if they did the drug? P(positive used)

4. P(positive used) = P(positive AND Used) P(Used) = 119 122 = 0. 975
P(positive used) = P(positive AND Used) P(Used) = = * This tells us that there is a 97.5% chance of testing positive if the person used the drug.

5. Example 2
What is the probability that a person used the drug given that they tested positive? P(used positive) = P(used AND positive) P(positive)

6. = 119 143 = 0.832 ** 83.2% chance that you used the drug if you tested positive.

7. Geometric Probabilities
Using areas of geometric figures to find probabilities.

8. What are the chances of landing inside the circle?4 4 15 5 30

9. Need to know areas
Area of circle = πr2 = π(25) = Area of rectangle = length x width = 30 x 15 = 450 So P(inside circle) = =

10. Complement Rule
What is the probability of landing OUTSIDE the circle? P(outside) = 1 – P(inside) = = .83