1. Bio-Statistic KUEU 3146 & KBEB 3153 Bio-Statistic Basic Probability Concerpts

2. Basic Probability What is Probability Probability Rules Counting Rules Venn Diagrams Contingency Table

3. What is Probability Probability is the ratio of number of ways the specified event can occur to the total number of equally likely events that can occur. i.e the no of favorable outcomes divide by the no of possible outcomes A probability of 1.0 means that the event will happen with certainly; 0 means that the event will not happen. If probability of is 0.5, the event should occur once in every two attempts on the average.

4. Probability (P) Dice: In a roll of a fair die, there are six equally possible outcomes i.e 1,2,3,4,5,6 (N=6). P(even number)= ? P(2 or 3)= ? P(greater than 3)= ?

5. Probability Rules P(A&B)= P(A).P(B) P(A|B)= P(A&B)/P(B) P(A or B)= P(A) + P(B) – P(A & B) Two events are independent if the occurrence of one has no effect on the chance of occurrence of the other. P(A|B)= P(A&B)/P(B)=P(A) Mutually exclusive events are events that cannot happen simultaneously.

6. Counting Rules Rule 1: Number of ways If an event A can occur in n distinct ways and event B can occur m ways, then the events consisting of A and B can occur in (n)(m) ways. Example choices of diet by amount of protein (low,medium,high) and by amount of fat (low,medium,high). There would be 9 different possible diets. Rule 2: Permutation The number of different ways in which n objects may be arranged is given by n! (n factorial). Example 3 types of treatment x,y,z. There would be 6 different possible treatment combination. 3!= 3.2.1 = 6 P(n,r)= n!/(n-r)! Or n P r = n!/(n-r)! Rule 3: Combinations A selection of a subgroup of distinct object, with order not being important. C(n,r)= n!/r!(n-r)! Or n C r = n!/r!(n-r)!

7. Venn Diagrams ( not E ) E ( A & B ) ( A or B ) A A B B

8. Contingency Table Professor (R1) Associate Professor (R2) Assistant Professor (R3) Instructor (R4) Total Under 30 (A1) 2357668 30-39 (A2) 5217016317402 40-49 (A3) 156125616348 50-59 (A4) 14568364253 60 & Over (A4) 75153093 Total430381320331164 RANK AGE

9. Contingency Table Marginal Probability, P(A) A1 = event the faculty member is under 30 years old which is 68 R2 = event the faculty member is an associate professor which is 381 P(A1)=68/1164=0.058 and P(R2)=381/1164=0.327 Joint Probability, P(A&B) A1&R2= event where the faculty member is an associate professor and under 30 years old which is 3. Therefore P(A1&R2)= 3/1164= 0.003 Conditional Probability, P(A|B) The probability that the faculty member selected is in his or her 50’s given than an assistant professor. P(A 4 |R 3 )=36/320=0.113