Using the document (attached) ,answer the questions about the possible role of confounders and effect modifiers and quantitatively assess the impact of confounders and effect modifiers on the results of a study. Please show all the work. Thank you!

Week 2 AssignmentQuestion 1Compute the weighted mean for the following data.[img width="223" height="151" src="https://content.grantham.edu/at/BA215/2015/wk-2-assignment-image-1.png"> If P(A) = 0.50, P(B) = 0.40, and P(A ∪ B) = 0.88, then P(B | A) =Question 3Six vitamin and three sugar tablets identical in appearance are in a box. One tablet is taken at random and given to Person A. A tablet is then selected and given to Person B. What is the probability thatPerson A was given a vitamin tablet?Person B was given a sugar tablet given that Person A was given a vitamin tablet?neither was given vitamin tablets?both were given vitamin tablets?exactly one person was given a vitamin tablet?Person A was given a sugar tablet and Person B was given a vitamin tablet?Person A was given a vitamin tablet and Person B was given a sugar tablet?NOTE: Please submit work in word dox.

Find the value of each annuity. Give your answer to the nearest dollar.Amount of DepositFrequency CompoundedRateNumber of YearsType of Annuity$500Annually6%30Ordinary$600Semiannually12%10DueFor purposes of compensation, an actuary working for a lawyer estimates the annual earnings of a September 11 victim that died at the Twin Towers at age 32.The victim was making $95,000 a year and a stream of payments for that amount would have likely accrued to him annually until retirement at age 65.The actuary knows that this is an ordinary annuity problem. He assumes, as is usual, that the victim's salary would grow in tandem with inflation, which for years has hovered at around at 3% annually.What is the future value of this annuity, the minimum basis for a possible settlement with the relatives of the victim if a fair settlement were indeed on the table?(Please note that, in court, the argument over compensation will likely be about the annuity's present value, as close relatives have immediate needs for cash; we will cover the concept of an annuity's present value next week and then return to this problem.)Belle and the Beast want to retire in 10 years and can save $2,000 every three months. They plan to deposit the money at the beginning of each quarter into an account paying 4% compounded quarterly. How much will they have in 10 years?Review the Art Space Tokyo project. Focus on the choice of rewardsHow is the choice justified?