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.

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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) Non-nursing majors 1016 1729 2745 Nursing majors Total Males Females Total 95 700 795 2429 3540 (a) Find the probability that the student is male or a nursing major. P (being male or being 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.)

Solution

(a)

P(male)= 1111/3540

P(nursing majors)= 795/3540

P(male and nuring majors)= 95/3540

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

P (being male or a being a nursing major)=(1111/3540)+(795/3540)-(95/3540)=1811/3540=0.512

(b)

P(female)= 2429 / 3540

P(not nursing major)= 2745 / 3540

P(female and not nursing major)= 1729 / 3540

P(being female or not being a nursing major)= P(female)+P(not nursing major)- P(female and not nursing major) = (2429/3540)+(2745/3540)-(1729/3540)=3445 / 3540 =0.973

(c)

P(not female)= 1111/3540

P(nursing majors)= 795/3540

P(not female and nuring majors)= 95/3540

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

P (not being female or a being a nursing major)=(1111/3540)+(795/3540)-(95/3540)=1811/3540=0.512

(d)

No because there are 95 males majoring in nursing.