STAT 1000 Lecture Notes - Lecture 24: Sample Space

• School: University of Manitoba
• Department: Statistics
• Course: STAT 1000
• Professor: Zenaida Mateo

Document Summary

Independent : observing the outcome of the first in no way alters the probability structure of the second. For example, the outcome of the roll of the first die is independent of the outcome of the second. That is, knowing the result of the first toss in no way affects the probability structure of the second toss. Two events a and b are independent if and only if. For the dice experiment, consider the following three events. S = {11,12,13,14,15, 16 ,21,22,23,24, 25 , 26 , 31,32,33,34, 35 ,36, 41, 42, 43, 44 , 45, 46, P (a b) = (cid:1005) (cid:1007)(cid:1010) (cid:1007)(cid:1010) P(a) p(b) = (cid:4666) (cid:1010) (cid:1007)(cid:1010)(cid:4667)(cid:4666) (cid:1010) (cid:1007)(cid:1010) (cid:4667)= (cid:1005) P (a c) = (cid:1007)(cid:1010)(cid:4667)(cid:4666) (cid:1009) (cid:1007)(cid:1010) (cid:4667)= (cid:1009) Therefore, since p (a b) p(a) p(c), a and c are not independent. (cid:1005) (cid:1007)(cid:1010) (cid:1006)(cid:1005)(cid:1010) Any probability is a number between 0 and 1, inclusive, i. e. 0 p(a) 1. An event with probability of 0 never occurs.