Answer: a) 14/65 b) 34/65
Step-by-step
Using set concept (venn diagram)
Let U be the total number if students
F be freshmen
E be economics majors
n(U) is the number of college class students i.e 65
n(F) to be number of freshmen i.e 36
n(E) to be economics major = 34
n(FuE)' be neither i.e 9
Students being both freshman and economics major is n(FnE) which is unknown
Prob ability that the student I both freshman and an economics major is n(FuE)/n(U)
To calculate n(FnJ), we use the formula
n(U) = n(F) + n(E) - n(FnE) + n(FuE)'
65 = 36 + 34 - n(FnE) + 9
65 = 79 - n(FnE)
n(FnE) = 14.
Probability = 14/65
b) If the student select economics major, probability that she is also a fresh men = n(E)/n(U) = 34/65 economics
That means that student studied economics and also among the freshmen :
