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

Answer:

$0.66$

Step-by-step 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 $=37\%=\frac{37}{100}\times100x$

                                                     $=37x$

voters registered as Republicans $=29\%=\frac{29}{100}\times100x$

                                                       $=29x$

voters registered as Green party $=7\%=\frac{7}{100}\times100x$

                                                       $=7x$

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

                                                                                    $=\frac{37x}{100x}=0.37$

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

                                                                                     $=\frac{29x}{100x}=0.29$

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 $0.66$