Conditional Probability and Geometric Probability

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)

Example Used Didn’t Drug Use Positive Test 119 24 Negative Test 3 154 What is the probability that someone tested positive if they did the drug? P(positive used)

P(positive used) = P(positive AND Used) P(Used) = 119 122 = 0. 975 P(positive used) = P(positive AND Used) P(Used) = 119 122 = 0.975 * This tells us that there is a 97.5% chance of testing positive if the person used the drug.

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)

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

Geometric Probabilities Using areas of geometric figures to find probabilities.

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

Need to know areas Area of circle = πr2 = π(25) = 78.54 Area of rectangle = length x width = 30 x 15 = 450 So P(inside circle) = 78.54 = .17 450

Complement Rule What is the probability of landing OUTSIDE the circle? P(outside) = 1 – P(inside) = 1 - .17 = .83