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}](https://img.qammunity.org/2023/formulas/mathematics/high-school/jddjkjg628vniueppr269d61ktlo8iwisg.png)
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}](https://img.qammunity.org/2023/formulas/mathematics/high-school/86f0lwhd1xvhuf0t0puc4wsulz4152zqa1.png)
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}](https://img.qammunity.org/2023/formulas/mathematics/high-school/nxsi563amlaino1smceww81ibtdypiaqc3.png)
Thus probability for the selected person is not unsure of tax and is female is 0.988.