Question

A) The table below shows the results of a survey that asked 1052 adults from a certain country if they would support a change in their​ country's flag. A person is selected at random. Complete parts​ (a) through​ (d).

	Support	Oppose	Unsure	Total
Males	151	332	10	493
Females	244	296	19	559
Total	395	628	29	1052

​(a) Find the probability that the person opposed the change or is female.

​(b) Find the probability that the person supports the change or is male.

​(c) Find the probability that the person is not unsure or is female.

(d) Are the events​ "being male" and​ "support" mutually​ exclusive? Explain.

A.​No, because one​ can't be male and support the change at the same time.

B.​No, because there are 151 males that support the change.

C.​Yes, because there are 151 males that support the change.

D.​Yes, because one​ can't be male and support the change at the same time

B) The table below shows the results of a survey that asked 2859 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts​ (a) through​ (e).

	Frequently	Occasionally	Not at all	Total
Male	227	458	796	1481
Female	202	430	746	1378
Total	429	888	1542	2859

​(a) Find the probability that the person is frequently or occasionally involved in charity work.

​(b) Find the probability that the person is female or not involved in charity work at all.

​(c) Find the probability that the person is male or frequently involved in charity work.

​(d) Find the probability that the person is female or not frequently involved in charity work.

​(e) Are the events​ "being female" and​ "being frequently involved in charity​ work" mutually​ exclusive? Explain.

A.​No, because no females are frequently involved in charity work.

B.​Yes, because 202 females are frequently involved in charity work.

C.​No, because 202 females are frequently involved in charity work.

D.​Yes, because no females are frequently involved in charity work.

C) 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	99	1018	1117
Females	600	1727	2327
Total	699	2745	3444

(a) Find the probability that the student is male or a nursing major.

(b) Find the probability that the student is female or not a nursing major.

​(c) Find the probability that the student is not female or a nursing major.

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

A.​Yes, because there are 99 males majoring in nursing.

B.​No, because there are 99 males majoring in nursing.

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

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

Answer 1

A)

P(person opposes change ) = 628/1052

P(person female) = 559/1052

P(person opposes change and female) = 296/1052

a) p( person opposes change or is female)

= P(person opposes change) + p(female) - p(person opposes change and female)

= 628/1052 + 559/1052 - 296/1052

= 891/1052

B)

P(person support change) = 395/1052

P(male) = 493/1052

P(person support change and male) = 151/1052

P(person support change or male)

= P(person support change) + p(male) - p(person support change and male)

= 395/1052 + 493/1052 - 151/1052

=737/1052

C)

P(person is not unsure) = 29/1052

P(female) = 559/1052

P(person is not unsure and female) = 19/1052

P(person is not sure or female)

= P(person is not sure) + p(female) - p(person is not sure and female)

= 29/1052 + 559/1052 - 19/1052

= 569/1052

D)

P(male) = 493/1052

P( support) = 395/1052

For mutually exclusive events p(male and support) should equal to zero

Here,

P(male and support) = 151/1052 which is not equal to zero

So,they are not mutually exclusive

Answer a) one cannot be male and support the change at same time.

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