Respuesta :
Answer:
[tex]0.66[/tex]
Step-by-step explanation:
GIVEN: Suppose that in a certain county [tex]37\%[/tex] of voters are registered as Democrats, [tex]29\%[/tex] as Republicans, [tex]7\%[/tex] as Green party, and the rest are considered Independents. You conduct a poll by calling registered voters in the county at random.
TO FIND: Probability that the first call will be to either a Democrat or a Republican.
SOLUTION:
Lets total population of county be [tex]100x[/tex].
voters registered as Democrats [tex]=37\%=\frac{37}{100}\times100x[/tex]
[tex]=37x[/tex]
voters registered as Republicans [tex]=29\%=\frac{29}{100}\times100x[/tex]
[tex]=29x[/tex]
voters registered as Green party [tex]=7\%=\frac{7}{100}\times100x[/tex]
[tex]=7x[/tex]
Probability that first call will be to Democrats [tex]P(A)=\frac{\text{total democrats}}{\text{total voters}}[/tex]
[tex]=\frac{37x}{100x}=0.37[/tex]
Probability that first call will be to Republican [tex]P(B)=\frac{\text{total republicans}}{\text{total voters}}[/tex]
[tex]=\frac{29x}{100x}=0.29[/tex]
probability that the first call will be to either a Democrat or a Republican
[tex]=P(A)+P(B)[/tex]
[tex]=0.37+0.29[/tex]
[tex]=0.66[/tex]
Hence the probability that the first call will be to either a Democrat or a Republican is [tex]0.66[/tex]
