Question

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 majors	Total
Males	9898	10141014	11121112
Females	700700	17241724	24242424
Total	798798	27382738	35363536

?(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.)

?(d) Are the events? "being male" and? "being a nursing? major" mutually? exclusive? Explain.

A. Yes, because there are 98males majoring in nursing.

B. No, because there are 98 males majoring in nursing.

C. No, because one? can't be male and a nursing major at the same time.

D. Yes, because one? can't be male and a nursing major at the same time.

Answer 1

a) P(being male or being nursing major)

P(Male) = 1112/ 3536

P(Nursing Major) = 798/3536

P(Male & Nursing Major) = 98/3536

P(Male or Nursing Major)= P(Male) + P(Nursing major)- P(M & NM)= (1112/3536) + (798/3536) - (98/3536)= 1812/3536= 0.512443

b) P(being female or not being a nursing major)

P(Female) =2424/3536

P(Not Nursing Major) = 1- P(Nursing major) =1- (798/3536)= 2738/3536

P(F & Not NM) = P(F)- P(F & NM)= ( 2424/3536) - (700)= 1724/ 3536

P(F or Not NM)= P(F) + P(Not NM) - P(F & Not NM)

P(F or Not NM)= (2424/3536)+(2738/3536) - (1724/3536)= (3438/3536)= 0.972285

c) P(Not Famale or Nursing Major)

P(Not F) = 1- P(F)= 1- (2424/3536)= 1112/3536

P(NM)= (798/3536)

P(Not F & NM)= P(NM)- P(F & NM)= (798/3536) - (700/3536)= 98/3536

P(Not F or Nursing Mjaor) = P(Not F) + P(NM) -P(Not F & NM)

P(Not F or Nursing Mjaor) = (1112/3536) + (798/3536) - (98/3536) = 0.512443

d)To be mutually exclusive events: P( A & B) = P(A) *P(B)

P(M & NM)= 98/3536 = 0.027715

P(M)*P(NM)= (1112/3536) *( 798/3536)= 0.070971

Both are not mutually exclusive.

No, because one? can't be male and a nursing major at the same time.