Question

Suppose that in a certain county 37% of voters are registered as Democrats, 29% as Republicans, 7% as Green party, and the rest are considered Independents. You conduct a poll by calling registered voters in the county at random. What is the probability that the first call will be to either a Democrat or a Republican?

Answer 1

`0.66`

Explanation:

GIVEN: Suppose that in a certain county
`37\%` of voters are registered as Democrats,
`29\%` as Republicans,
`7\%` 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
`100x`.

voters registered as Democrats
`=37\%=(37)/(100)*100x`

`=37x`

voters registered as Republicans
`=29\%=(29)/(100)*100x`

`=29x`

voters registered as Green party
`=7\%=(7)/(100)*100x`

`=7x`

Probability that first call will be to Democrats
`P(A)=\frac{\text{total democrats}}{\text{total voters}}`

`=(37x)/(100x)=0.37`

Probability that first call will be to Republican
`P(B)=\frac{\text{total republicans}}{\text{total voters}}`

`=(29x)/(100x)=0.29`

probability that the first call will be to either a Democrat or a Republican

`=P(A)+P(B)`

`=0.37+0.29`

`=0.66`

Hence the probability that the first call will be to either a Democrat or a Republican is
`0.66`