A survey is made in a neighborhood of 80 voters.65 were Democrats and 15 were Republicans.Of the Democrats,35 are women,while 5 of the Republicans are women.If one subject from the group is randomly selected,find the probability: The individual is either a woman or a Democrat.

Question

Quizplus · Accepted Answer

We can use the formula for finding the probability of the union of two events:
P(A or B) = P(A) + P(B) - P(A and B)
where A and B are two events.

Let A be the event that the individual is a woman and B be the event that the individual is a Democrat. Then, we can find the probabilities as follows:

P(A) = Number of women / Total number of voters = 40 / 80 = 0.5
P(B) = Number of Democrats / Total number of voters = 65 / 80 = 0.8125
P(A and B) = Number of women who are Democrats / Total number of voters = 35 / 80 = 0.4375

Substituting these values in the formula, we get:

P(A or B) = 0.5 + 0.8125 - 0.4375
= 0.875

Therefore, the probability that the individual is either a woman or a Democrat is 0.875 or 87.5%. The best choice is (E).

A Survey Is Made in a Neighborhood of 80 Voters