Please SHOW ALL WORK this is specifically asked as LONG ANSW

Please SHOW ALL WORK, this is specifically asked as LONG ANSWER QUESTION.

1.Use the following two-way table classifying Foothill students\' major and unit status to find the probability requested in each question. Give vour answer as an unreduced fraction and as a decimal appropriately rounded to 3 decimal places Major Arts Student Part Time |11 Units Full Time 17 28 AA Science AS Science Undecided 30 52 82 Student Part Time 17 28 60 92 152 14 a)The probability that a randomly chosen student is a part time student b)The probability that a randomly chosen is a full time student given that the student is an AA Science major c) The probability that a randomly chosen student is either part time or is undecided d) The probability that a randomly chosen student is both part time and undecided. e) The probability that a randomly chosen student is not undecided.|

Solution

a. The probability that a randomly chosen student is a part time student =

Total number of Student Part Time / Total number of students = 60/152 = 0.395

b. The probability that a randomly chosen is a full time student given that the student is an AA Science major

= Number of full time students with AA science major / Total students with AA science major

= 52/82 = 0.634

c. The probability that a randomly chosen student is either part time or is undecided

= Total number of students who are either part time or is undecided / Total number of students

= (60+6)/152 66/152 = 0.434

d. The probability that a randomly chosen student is both part time and undecided.

= Total number of students who are part time and undecided / Total number of students

= 8/152 = 0.053

e. The probability that a randomly chosen student is not undecided.

= 1 - probability that a randomly chosen student is undecided.

= 1 - (14/152) = 138/152 = 0.908