Introduction to Probability Problem 1 Problem 1 Construct a

Introduction to Probability Problem 1

Problem 1 Construct a valid sample space for the following experiments, specifying if it is a finite, infinite or continuous (uncountable) number of outcomes. If it is finite, indicate what is its size. 1. The number of lethal and non-lethal accidents among the next 4 flights out of PHX Assume three possible cases are reported for each flight: 1) no accident; 2) non-lethal accident; 3) lethal accident. 2. The latitude and longitude of someone\'s birth place 3. Three consecutive coin tosses. 4. The number of times my Mom has to call before I answer

Solution

1). Let us denote no accident as A

    Let us denote Non-lethal accident as B

    Let us denote lethal accident as C

For each fligh there can be three cases either A,Bor C

so sample space is {AAAA,AAAB,AABA,ABAA,BAAA,AAAC,AACA,ACAA,CAAA,AABC,AACB,ABCA,ACBA,BCAA,CBAA,BAAC,CAAB,BBBB,BBBA,BBAB,BABB,ABBB,BBBC,BBCB,BCBB,CBBB,BBAC,BBCA,BACB,BCAB,ACBB,CABB,ABBC,CBBA,CCCC,CCCA,CCAC,CACC,ACCC,CCCB,CCBC,CBCC,BCCC,CCAB,CCBA,CABC,CBAC,ABCC,BACC,ACCB,BCCA}

Finite-42 sample space

2.) IN 360 degree anfle of earth there can be many infinte no of Lattitude and Longitude Position which cannot be written as sample space so infinite sample space will be there.

3.) There are 2 Possibilities for a toss of a coin-H(head) or Tail(T)

so sample space is

{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

FINITE SAMPLE SPACE-8

4.) Infinte sample space

Let us denote you answer as A

and u dnt answer as B

so infinte sample space be like

{A,BA,BBA,BBBA,BBBBA,...........}