Question

The shows the result of a survey that asked 1054 adults from a certain country if they favored or opposed a tax to fund education. A person is selected at random. Complete parts (a) through (c).10De1320a)Fohe taxePotetordeRestas() he probably the persone e tax or se malePo the terme)the resthasProm(Roth)chotthewwer boxes

Answer 1

The number of females are F = 553.

The number of persons who oppose the tax is, O = 629.

The total number of person is, T = 1054.

The number of person who are femal and oppose the tax is, (O and P) = 297.

Determine probability for selected person is female or oppose the tax.

`\begin{gathered} P(OorP)=P(O)+P(F)-P(OandP) \\ =(629)/(1054)+(553)/(1054)-(297)/(1054) \\ =(629+553-297)/(1054) \\ =(885)/(1054) \\ =0.8396 \\ \approx0.840 \end{gathered}`

Thus probability for the selected person to be female or oppose the tax is 0.840.

PART (B)

The number of persons are male is M = 501.

The number of person in support of tax is S = 392.

The number of person support the tax and are male is (S and M) = 156.

Determine the probability for selected person supports the tax and is male.

`\begin{gathered} P(SorM)=P(S)+P(M)-P(SandM) \\ =(392)/(1054)+(501)/(1054)-(156)/(1054) \\ =(392+501-156)/(1054) \\ =(737)/(1054) \\ =0.6992 \\ =0.699 \end{gathered}`

Thus probability for selected person to be men or in support of tax is 0.699.

PART C

The number of person not unsure of tax is N = 1021.

The number of female is F = 553.

The number of person who are femal and not unsure of tax is (N and F) = 533.

Determine the probability for selected person is not unsure or is female is,

`\begin{gathered} P(NorF)=P(N)+P(F)+P(NandF) \\ =(1021)/(1054)+(553)/(1054)-(533)/(1054) \\ =(1021+553-533)/(1054) \\ =(1041)/(1054) \\ =0.9876 \\ \approx0.988 \end{gathered}`

Thus probability for the selected person is not unsure of tax and is female is 0.988.