1. Psychology 290 Lab 10 – Probability Feb. 6 – 8. 2007 Probability Mutually Exclusive Additive Rule Multiplicative Rule (joint probability) With or without replacement

2. Equations Probability of a event –P(A) = # of A outcomes / total # of outcomes Additive Rule –P(A or B) = P(A) + P(B) – P(A and B) [Subtraction required in the case of non-mutually exclusive events] Multiplicative Rule –P(A and B) = P(A) x P(B) – P(A

3. Basic Examples The statistics club has twelve members, 7 psychology students, 2 math students, and 3 science students. Two of the psychology students are female, 1 of the math students are female, and all of the science students are female. a). What is the probability of choosing a science student Total # of students = 12 # of science students = 3 p (science student) = 3/12 = 1/4 (25%)

4. Basic Example cont. The statistics club has twelve members, 7 psychology students, 2 math students, and 3 science students. Two of the psychology students are female, 1 of the math students are female, and all of the science students are female. a). What is the probability of choosing a male student Two psych students are female  5 are male One math student is female  1 is male All science students are female  0 male p (male student) = 6/12 = 1/2 (50%)

5. Additive Rule Example A bag of fruit contains 6 apples, 3 oranges, 5 plums, and 6 mangoes. What is the probability of pulling out an apple or a mango? p (apple or mango) = p (apple) + p (mango) – p (apple & mango) p (apple or mango) = 6/20 + 6/20 – 0 = 12/20 = 3/5 (60%)

6. Additive Rule Example Using a standard deck of cards, what is the probability of choosing a club or an ace? p (club or ace) = p (club) + p (ace) – p(club & ace) p (club or ace) = 13/52 + 4/52 – p (club) * p (ace) p (club or ace) = 17/52 – (13/52 * 4/52) p (club or ace) = 17/52 – 1/52 p (club or ace) = 16/52  4/13 (~31%)

7. Multiplicative Rule Example A bag of fruit contains 6 apples, 3 oranges, 5 plums, and 6 mangoes. What is the probability of pulling out a plum and then an orange (with replacement)? p (plum & orange) = p (plum) * p (orange) p (plum & orange) = 5/20 * 3/20 p (plum & orange) = 15/400 = 0.0375 (3.75%) What is the probability of pulling out a plum and then an orange (without replacement)? p (plum & orange) = p (plum) * p (orange) p (plum & orange) = 5/20 * 3/19 p (plum & orange) = 15/380 = 0.0395 (3.95%)