Can someone please answer 14 I need help please show work F

Can someone please answer 1-4 . I need help. please show work

For each of the below exercises, circle the correct answer and provide justifications if required. Problem 1. The table below shows the political affiliation of 1000 randomly selected American voters and their positions on the school of choice program: What is the Probability that a randomly selected voter is neither a Republican nor Favors the school of choice program? A. 0.14 B. 0.5 C. 1.0 D. 0.16 E. None of the above. Problem 2-3. According to the American Social Health Organization (ASHO), one put of four teens in the United States becomes infected with an STD each year. 2. What is the probability that in a random selection of 7 teens no one becomes infected with an STD in a given year? A. 0.25 B. 0.75 G. 0.2236 D. 0.1335 E. None of the above 3. What is the probability that in a random selection of 4 teens at least one be comes infected with STD in a given year? A. 0.316 B. 0.683 C. 0.974 D. 0.683 E. None of the above Problem 4. in a game, a spinner with five equal-sized spaces is labeled from A to E. If a player spins an A or an E the player wins 15 points. If any other letter is spun the player loses 4 points. What is the expected gain or loss from playing 40 games? A. Gain of 55 B. Gain of 144 C. Gain of8 D. Loss of 1 E. Loss of 8

Solution

1)

total number of voters = 1000

number of voters who is neither republican nor favours

                                                = number of democrats who oppose + number of others who oppose

                                                  = 40 + 100 = 140

probability of a selectd voter is neither Republican nor in favour

= 140/1000 = 0.14

hence A is the correct choice

2)

let X be random variable which represents teen infected with STD

X follows binomial distribution

proportion of teens infected with STD = 1/4 = 0.25

P(X=0) = 7C0 * 0.25^0 * (1-0.25)^7

= 0.1335

hence D is the correct choice

3)

P(X>=1) = 1 - P(X<1)

= 1 - P(X=0) - P(X=1)

= 1 - 4C0 * 0.75^4 - 4C1 * 0.25 * 0.75^3

= 0.2617

hence E is the correct choice

4)

probability of landing on any space = 1/5

expected gain from each game = 1/5 * 15 + 1/5 * (-4) + 1/5*(-4) + 1/5 *(-4) + 1/5 * 15

= 3.6

expected gain from 40 games = 3.6 * 40 = 144

hence B is the correct choice