MA 120
E. Lee
Summary(4.1-4.5)
Chapter 4 - Probability and Probability distribution
1. Probability = chance
experiment, event, simple event(an event that cannot be decomposed), sample space,
probability
Example 1) When tossing a die once, what is the probability to get odd number(s)?
experiment: toss a die and observe the number that appears on the upper face
event: observe an odd number = {1,3,5}
sample space(S) = the set of all simple events={1,2,3,4,5,6}
probability of the event = numbers in the event
numbers in the sample space =3
6=1
2
Note:
(a) Each probability must lie between 0 and 1.
(b) Probability of the sample space = P(S) = 1
2. Useful counting rules
(a) n! = n(n−1)(n−2) · · · (3)(2)(1) = n(n−1)! = n(n−1)(n−2)!
Example 2) 3! = 6! = 0! = 1, 1! = 1
(b) Pn
r=n!
(n−r)! (number of ways we can arrange rout of n)
Example 3) P3
2=3!
(3 −2)! =(3)(2)(1)
1! = 6, P3
3=
(c) Cn
r=n!
r!(n−r)! (number of ways we can choose rout of n)
Example 4) C3
2=3!
2!(3 −2)! =(3)(2)(1)
(2)(1)(1) = 3, C8
3=
