1.A roulette wheel has 38 pockets: 36 are numbered 1 through 36 while the other two are labeled '0' and '00'.Eighteen of the pockets number 1 through 36 are black while the other 18 are red.The pockets labeled '0' and '00' are green.To play roulette, a metal ball is spun around the wheel and eventually lands in one of the pockets.

Gamblers have a number of options for betting.They can bet on the individual pocket that the ball will land in, each with probability.They can bet on if the ball will land in the first 12, second 12, or third 12 (with '0' and '00' as other possible outcomes).Other options include betting on the color (red, black, or green), 1-18 or 19-36, or even or odd (with '0' and '00' considered neither even nor odd).Payouts are awarded to gamblers according to the type of bet they place with higher winnings for more unlikely events.

a.What is the probability that the ball does not land in a green pocket?

b.What is the probability that the ball lands in a pocket that contains thedigit'3' somewhere in the number?(Note: You are not finding the probability that it lands in the pocket '3'.)

c.Suppose the wheel is spun five times.What is the probability that the ball lands in a black pocket all five times?Assume spins are independent of one another.(This happened to me when I was in Las Vegas in 2018.I had money on red all five times...)

d.Suppose the wheel is spun twice.What is the probability that the ball lands in a red pocket at least once?Assume spins are independent of one another.

e.Suppose the wheel is spun twice.On the first spin, you place two bets: one on even and one on the first 12.On the second spin, you also place two bets: one on the third 12 and one on the pocket '13'.What is the probability that you win on both spins?(Hint: This is a complicated problem.Break it down into three separate calculations.)

2.In a poll taken in May 2019, 46% of people identified as Independents, while 31% identified as Democrats and 23% as Republicans.The same poll also asked respondents about if they were satisfied with the job that Donald Trump was doing as president.90% of Republicans approved of the job he was doing compared to 33% of Independents and 9% of Democrats.

a.Either draw the probability tree showing support for the job Donald Trump is doing as president or complete the given probabilities.

b.What is the probability that a randomly selected person approves of the job of Donald Trump regardless of political affiliation?

c.Given that a person approves of the job of Donald Trump, what is the probability that they are an Independent?

d.Given that a person does not approve of the job of Donald Trump, what is the probability that they are a Democrat?

e.Suppose a randomly selected person is chosen.What is the probability that they are a Republican or approve of the job of Donald Trump?