4.49 Two thousand randomly selected adults were asked if they are in favor of or

Question

4.49 Two thousand randomly selected adults were asked if they are in favor of or against cloning. The following table gives the responses In Favor 395 300 Against 405 680 No Opinion 100 120 Male Female a. If one person is selected at random from these 2000 adults, find the probability that this person is i. in favor of cloning ii. against cloning ii. in favor of cloning given the person is a female iv. a male given the person has no opinion h. Are the events "male"and "in favor" mutually exclusive? What about the events "in favor" and against?" Why or why nor? e. Are the events "female" and "no opinion" independent? Why or why not?

Explanation / Answer

a) (i)P(in favour) =695/2000 = 0.3475

(ii)P(against cloning) =1085/2000 =0.5425

(iii)P(in favour|female) =300/1100 =0.2727

(iv)P(male|no opinion) =100/220 =0.4545

b)

male and in favour are not mutually exclusive as they contain 395 common opinion between them

in favour and against are mutually exclusive as they contain no common opinion between them

c)

P(female) =1100/2000 =0.55

P(no opinion)=220/2000 =0.11

P(female and no opinion)=120/2000 =0.06

as P(female)*P(no opinion) =0.55*0.11 =0.0605 which is not equal to P(female and no opinion).

therefore female and no opinion are not independent,

in favor against no opinion total male 395 405 100 900 female 300 680 120 1100 total 695 1085 220 2000

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