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Lecture

# Stats 141 Probability.docx

Department
Statistics
Course Code
STAT141
Professor
Beda Dessens

Page:
of 4 Stats 141
Example:
There are six socks in a drawer. Two are yellow, two are green, and two are purple. If two socks
are drawn at random (socks are not replaced), what is the probability that...?
A.) Both are yellow
P(Sock 1 yellow and Sock 2 yellow)
   
B.) Both same colour
P(Sock 1 and Sock 2 same colour)
  
 
C.) First is yellow and the second is not yellow
P(First sock yellow and second sock not yellow)
  
   
Example 2:
Same information as Example 1 but with replacement.
A.) Both yellow
P(Both yellow)
  
   
B.) Both same colour
P(Sock 1 and sock 2 are same colour)
 
   
C.) First is yellow and the second is not yellow
P(First yellow and second not yellow)
  
   
Example 3:
The chance a car turns left at an intersection is 30%.
What is the probability at least one of the next 4 cars turns left.
Assume the chance of any one car turning left is independent of any other.
 
 
               
    
  
  
  
 
Continuous Distribution
- Has to do with area under the curve
      
    
  
Side note: In discrete: 
Uniform Distribution
  
Example:
Arrival times of an aircraft are uniformly distributed between -5 and 10 minutes.
A.) Draw the graph that represents this distribution
 
B.) What is the density function ?
    
 
  
  
C.) What is the probability the plane is early?
  
        
D.) What is the chance the plane arrives between 5-8 minutes late?
         
E.) What is the expected arrival time of the plane?