Statistics and Data Analysis

3-1:  Consider the experiment of drawing two cards from a deck in which all picture cards have been removed and adding their values (with ace = 1). 

 a.  Describe the outcomes of this experiment. List the elements of the sample space. 

 b.  What is the probability of obtaining a total of 5 for the two cards? 

 c.  Let  A be the event “total card value is 5 or less.” Find  P ( A ) and  P ( A c ).  Tips: You have cards from 1-10 in four different types; spades, diamonds, clubs, and hearts. Tp get the sample space you need to consider all combinations of a certains sum; for example, sum value of 2 could be:  [1 spades + 1 diamonds], [1 spades+1 clubs], [1 spades+ 1 hearts], 1 diamonds + 1 clubs, 1 diamonds + 1 hearts, 1 diamonds + 1 spades, 1 clubs +1 hearts, 1 clubs +1 spades, 1 clubs + 1 diamonds, 1 hearts + 1 spades, 1 hearts + 1 diamonds, 1 hearts +1 clubs
as u see the total possibilities of sum 2 is 12. You will need top repeat same method for sum of 3, 4, etc. 3-5: An airline tracks data on its flight arrivals. Over the past six months, 25 flights on one route arrived early, 150 arrived on time, 45 were late, and 30 were cancelled. 

 a.  What is the probability that a flight is early? On time? Late? Cancelled? 

 b.  Are these outcomes mutually exclusive? 

 c.  What is the probability that a flight is either early or on time? 

Please be sure your work is organized, legible, and your responses are substantive. You need to submit all details of your work including excel sheets used to arrive to the solution. It is not enough to attach your excel sheet. You MUST provide interpretation of results and describe conclusions.