Microsoft Word - Test #2 1 MAT 200 Probability & Statistics Test #2 Name (Printed)_________________________________ Show your work to receive full credit. Work must include formulas as well as the...

i just need the problems worked and sent back to me.


Microsoft Word - Test #2 1 MAT 200 Probability & Statistics Test #2 Name (Printed)_________________________________ Show your work to receive full credit. Work must include formulas as well as the values used in the formula. The work must be mathematically sound and mathematically logical. 1) An UNO deck consists of 108 cards, of which there are 76 Number cards, 8 Skip cards, 8 Reverse Cards, 8 Draw two cards, 4 Draw four cards and 4 Wild cards. a) (5 points) If you select one card out of the deck of Uno cards, what is the probability of selecting a Draw Four Card ? b) (5 points) Assume two cards are selected in sequence one after the other without replacement from a UNO deck. What is the probability of selecting a Skip card first and then (without replacing the first card back in the deck) selecting a Reverse Card second? 2 Name (Printed)_________________________________ 2) (5 points) If there are 3 green balls, 4 red balls, and 10 blue balls in a basket, what is the probability that you will pick out a red ball? 3) (5 points) A class has 30 students. Out of the thirty students, twenty-four are males. Assuming all of the students have an equal chance of being selected, find the probability of selecting a female. (Only one person is selected) 3 Name (Printed)_________________________________ 4) (5 points) How many ways can we pick a team of 4 people from a group of 8 and the order that we pick them does not matter? 5) (5 points) A company is hiring two different positions: an engineer and a manager. How many ways can these positions be filled if there are 12 people applying for the engineer position and 17 people are applying for the manager position? 4 Name (Printed)_________________________________ 6) (5 points) Assume a license plate have three letters followed by four digits. Assuming that any letter or digit can be used, how many different license plates are possible? (Reminder, there are 26 letters in the alphabet and there are 10 digits to choose from between 0 through 9 Illustration of a license plate _________ __________ _________ _________ ___________ Letter (A-Z) Letter (A-Z) Letter (A-Z) Digit (0-9) Digit (0-9) How many different license plates are possible? 7) (1 points) Multiple Choice. The probability that two dependent events A and B will occur in sequence is a) P(A and B) = P(A) x P(B|A) b) P(A and B) = P(A) x P(B) c) None of the above 5 Name (Printed)_________________________________ 8) (5 points) The Kentucky Derby is a horse race held annually in Louisville, Kentucky. It is often referred to as The Greatest Two Minutes in Sports. People usually place bets on the horses and the order that they finish. One type of bet is called an exacta bet. The exacta bet requires you to select the top two finishers in the correct order. If there are 20 horses in the Kentucky Derby, how many different ways can the 20 horses finish first and second? 9) (5 points) Of the cartons produced by a company, 10% have a puncture, 15% have a smashed corner, and 2% have a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. 6 Name (Printed)_________________________________ 10) (3 points each) The table shows the number of earned degrees by level and gender conferred at GMC in a historical year. Gender Male Female Total Level of Degree Associates 275 453 728 Bachelors 650 875 1525 Masters 238 366 604 Doctoral 30 30 60 Total 1193 1723 2917 A person who earned the degree in the year is randomly selected. Find the probability of selecting someone who a) earned a bachelors degree b) earned a bachelors degree given that the person is a female c) earned a bachelors degree given that the person is not a female d) earned an associates degree or a bachelors degree e) earned a doctorate given that the person is a male f) earned a master’s degree or is a female g) earned an associate’s degree and is a male h) earned a bachelor’s degree and is a female 7 Name (Printed)_________________________________ 11) (5 points) A study found that 13% of people can wiggle their ears. Two unrelated people are selected at random without replacement. Assume that the first person is person A and the second person is person B. What is the probability that person A and person B can both wiggle their ears? 12) (5 points) A lottery has 52 numbers. In how many different ways can 6 of the numbers be selected? Assume that the order of the number does not matter. 13) (5 points) At Atlanta Speedway, 43 cars race cars entered the race. How many ways can the cars finish first, second, and third? (The order matters) 8 Name (Printed)_________________________________ 14) (5 points each) The percent of adults who say oatmeal raisin is their favorite cookie is ten percent. You randomly select 12 adults and ask them to name their favorite cookie. a) . Find the probability that the number who say oatmeal raisin is their favorite cookie is exactly four. Find P(X=3) b) Find the probability that the number who say oatmeal raisin is their favorite cookie is less than four. P(x < 4)="" c)="" find="" the="" probability="" that="" the="" number="" who="" say="" oatmeal="" raisin="" is="" their="" favorite="" cookie="" is="" at="" least="" 4.="" find="" p(x="" ≥="" 4)="" 9="" name="" (printed)_________________________________="" 15)="" (5="" points="" each)="" seventy="" percent="" of="" married="" couples="" paid="" for="" their="" honeymoon="" themselves.="" you="" randomly="" select="" 20="" married="" couples="" and="" ask="" them="" if="" they="" paid="" for="" their="" honeymoon="" themselves.="" a)="" find="" the="" probability="" that="" the="" number="" of="" couples="" who="" say="" they="" paid="" their="" honeymoon="" themselves="" is="" exactly="" 1.="" find="" p="" (x="1)" b)="" find="" the="" probability="" that="" the="" number="" of="" couples="" who="" say="" they="" paid="" their="" honeymoon="" themselves="" is="" more="" than="" 1.="" find="" p="" (x=""> 1) c) Find the probability that the number of couples who say they paid their honeymoon themselves is at most 1. Find P (X ≤ 1) 10 Name (Printed)_________________________________ 16) (3 points) The probability that an event will happen is P( E ) = 0.55 Find the probability that the event will not happen? 17) (3 points) The probability that an event will not happen is P( E’ ) = 0.13 Find the probability that the event will happen 18) (2 points) Multiple choice A survey found that 17% of US males say that Google New is a major source of news for them. You randomly select four adults and ask them whether Google is a major source of new for them. In order to find the probability that fewer than two of them respond, you can use the complementary event of x is less than 2. Which of the following is another way to write this complementary event? a) P(x<2) =="" p(2)="" +="" p(3)="" +="" p(4)="" b)=""><2) =="" p(3)="" +="" p(4)="" c)=""><2) =="" 1="" –="" [p(2)="" +="" p(3)="" +="" p(4)]="" d)=""><2) = 1 – [p(3) + p(4)] =="" 1="" –="" [p(3)="" +="">