Show work for all your solutions to the following problems. 1. Every week at Granny's senior community meeting there are 50 lottery tickets available for $1 each. They always sell out and Granny always buys one ticket. In this lottery, a single ticket is drawn and that person wins $25 while the senior community keeps the other $25 for community center improvements. a) Over the next 10 weeks, what is the chance that Granny never wins the lottery? b) Over the next 10 weeks, what is the chance that Granny wins the lottery at least one time? 2. Consider problem 1). a) If Granny buys a ticket and it is not drawn, then she loses her $1 which is the same as winning -1 dollars. But if her ticket is drawn, she wins $25 - $1 = +24 dollars. If I want to construct a box model to represent a single play of the lottery then the box will have tickets with -1 (winnings of negative $1) on them and tickets with 24 (winnings of positive $24) on them. Draw this box model. b) For the box in a) the box average is and the box SD is c) Granny thinks she will play her senior community's lottery about 400 times over the next five years. If I want to use the box model constructed above, should you conceptualize the 400 draws as with replacement or without replacement? Circle the correct answer. No explanation is required. d) If Granny plays her senior community's lottery 400 times, then she expects to win a total of dollars give or take e) In 400 plays of this lottery, what is the approximate chance that Granny loses less than $150? That is, what is the chance that Granny's total winnings are more than -150? () Suppose that Granny does play the lottery 400 times and wins only 6 times. What are her observed "winnings' If she won 6 times but lost 394 times? What is the chance error in this "winnings' outcome? (Hint: recall that her observed 'winnings' = expected winnings + chance error)