Extra Credit Due Wednesday December 13th by 1pm Math 104, Fall 2017 1. Jessica t
ID: 3148531 • Letter: E
Question
Extra Credit Due Wednesday December 13th by 1pm Math 104, Fall 2017 1. Jessica teaches 3rd boys including Jake and Michael. Before the class can go to play, they have to line up along the wall. (a) How many different ways are there for the class to line up? (b) How many ways can the class line up so that no two boys are next to each other? (c) How many ways can the class line up so that Jake is right behind Julia and Michael is right in front of Sarah? 2. A farmer owns a 2000-acre farm and can plant any combination of two crope: corn and soybeans. Corn requires 1 person day of labor and $90 capital for each acre planted, while soybeans requires 2 person days of labor and $30 of capital for each acre planted. Corn produces $170 in revenue per acre, and soybeans produce $190 in revenue per acre. The farmer has 3000 person days of labor available for the year, and he plans to spend at least $90,000 in capital. How many acres of each crop should the farmer plant in order to maximize the total revenue? 3. 11 people including Audifax and Hermione have entered a contest. First prize is backstage passes to the concert of their choice, second prize is a CD box set, and third prize is a gift card. Assume that the winners are chosen randomly (a) What is the probability that Audifax wins something? (b) What is the probability that Hermione wins the backstage passes given that Audifax wins something? (c) Are the two events "Audifax wins something" and "Hermione wins the backstage passes" independent? 4. Anna Graham is the competitive tiddlywinks champion at Cambridge. She is so skilled that when she tries to get a wink into the pot, she is successful 84% of the time. (a) Anna shoots 100 winks in a row. Let X be a random variable that assigns to each outcome the number of successful (wink goes in pot) shots. What is the expected (b) If Anna shoots 10 winks in a row, what is the probability that she missed more 5. A table has 2 boxes on it. Box A contains 3 red balls, 3 green balls and 1 white ball. value of X? than once? Box B contains 4 red balls, and 2 white balls. An unfair coin with pr[H]=0.7 is flipped. If the coin come up heads, two balls are chosen at random, one after the other, without replacement from Box A. If the coin comes up tails, two balls are chosen at random, one after the other, without replacement from Box B. A random variable X is assigned which keeps track of the total number of red balls chosen. Find the probability density function for XExplanation / Answer
(a)
(it is a problem to arrange 16 objects in 16 positions = P(16,16) = 16!/(16-16)! = 16!
no. of ways to put 16 students in line = 16! = 20,922,789,888,000
(b)
piegon hole method - place 7 boys and 9 girls in alternate positions
no. of ways = 7! * 9! * 2 = 3,657,830,400
(c)
Treat Jake and Julia as one object and also Michael and Sarah as another object.
Rest we have 12 objects
so total ways = (12+2) ! = 14!
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