The table below shows the number of male and female students

The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d) :

Nursing majors Non nursing major Total

Male 99 1017 1116

Female 600 1721 2321

Total 699 2738 3437

a Find the probability that the student is male or a nursing major P (being male or a being a nursing major) (Round to the nearest thousandth as needed)

b Find the probability that the student is female or not a nursing major P(being female or not being a nursing major) (Round to the nearest thousandth as needed)

c Find the probability that the student is not female or a nursing major P (not being female or being a nursing major (Round to the nearest thousandth as needed)

D Are the events \"being male\" and \"being a nursing major\" mutually exclusive? Explain a No because there are 95 males majoring in nursing b Yes because there are 95 males majoring in nursing c Yes because one can\'t be male and a nursing major at the same time

(a)

P(male)= 1116/3437

P(nursing majors)= 699/3437

P(male and nuring majors)= 99/3437

So the probability that the student is male or a nursing major is

P (being male or a being a nursing major)=(1116/3437)+(699/3437)-(99/3437)=1716/3437=0.499

(b)

P(female)= 2321 / 3437

P(not nursing major)= 2738 / 3437

P(female and not nursing major)= 1721 / 3437

P(being female or not being a nursing major)= P(female)+P(not nursing major)- P(female and not nursing major) = (2321/3437)+(2738/3437)-(1721/3437)=3338 / 3437 =0.971

(c)

P(not female)= 1116/ 3437

P(nursing majors)= 699/3437

P(not female and nursing majors)= 99/3437

So the probability that the student is not female or a nursing major is

P (not being female or a being a nursing major)=(1116/3437)+(699/3437)-(99/3437)=1716/3437=0.499

(d)

No because there are 95 males majoring in nursing.