A survey is being conducted in a county where 62% of the voters are Democrats and 38% are Republican. (a) What is the probability that two independently surveyed voters would both be Democrats?

0.3844 = 38.44% probability that two independently surveyed voters would both be Democrats

Step-by-step explanation:

For each voter, there are only two possible outcomes. Either the voter is a Democrat, or he is not. The probability of the voter being a Democrat is independent of other voters. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

62% of the voters are Democrats

This means that

(a) What is the probability that two independently surveyed voters would both be Democrats?

This is P(X = 2) when n = 2. So

0.3844 = 38.44% probability that two independently surveyed voters would both be Democrats

slope =

Step-by-step explanation:

Calculate the slope m using the slope formula

m =

with (x₁, y₁ ) = (- 8, 1) and (x₂, y₂ ) = (8, 9) ← 2 points on the green line

m = = =

Repeat with (x₁, y₁ ) = 0, 6) and (x₂, y₂ ) = (2, 7) ← 2 points on the blue line

m = =

Since the slopes of both lines are equal, then the lines are parallel