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Proper Subset - Finite Math - Exam, Exams of Mathematical Methods for Numerical Analysis and Optimization

Baddi University of Emerging Sciences and TechnologiesMathematical Methods for Numerical Analysis and Optimization

Main points of this exam paper are: Lottery, Two Daughters, Difference, Department, Mathematics, Faculty Members, Committees

Typology: Exams

2012/2013

Uploaded on 03/31/2013

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Spring 99 Math 110 Exam 1 Prof. Brick
Do the problems in order in your bluebook. Show your work.
1. Use a Venn diagram to determine whether the following is a valid syllogisms:
College classes are fun.
Math 110 is a college class.
Therefore, Math 110 is fun.
2. State the contrapositive of “If this is your favorite class then you will do well.”
3. Use a truth table to determine whether or not the wffs p→qand (¬p)∨qare equivalent.
4. Draw a Venn diagram for two sets Aand B(in a universal set U) for which Ais a
non-empty proper subset of B. In it shade the region B∩Ac.
5. No area code (a 3-digit number) can start with either a 0 or a 1. How many possible
area codes there are ? (Don’t worry about any other restrictions that the phone company
might use.) Explain your answer.
6. How many (5 card) poker hands have at exactly three kings ? Explain your answer.
7. From a group of nine men and five women, you wish to form a committee of three men
and two women. How many different committees can you form ? Explain your answer.
8. Find the probability of getting at least two heads when flipping a coin three times.
Explain your answer.
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Download Proper Subset - Finite Math - Exam and more Exams Mathematical Methods for Numerical Analysis and Optimization in PDF only on Docsity!

Do the problems in order in your bluebook. Show your work.

  1. Use a Venn diagram to determine whether the following is a valid syllogisms: College classes are fun. Math 110 is a college class. Therefore, Math 110 is fun.
  2. State the contrapositive of “If this is your favorite class then you will do well.”
  3. Use a truth table to determine whether or not the wffs p → q and (¬p)∨q are equivalent.
  4. Draw a Venn diagram for two sets A and B (in a universal set U ) for which A is a non-empty proper subset of B. In it shade the region B ∩ Ac.
  5. No area code (a 3-digit number) can start with either a 0 or a 1. How many possible area codes there are? (Don’t worry about any other restrictions that the phone company might use.) Explain your answer.
  6. How many (5 card) poker hands have at exactly three kings? Explain your answer.
  7. From a group of nine men and five women, you wish to form a committee of three men and two women. How many different committees can youform? Explain your answer.
  8. Find the probability of getting at least two heads when flipping a coin three times. Explain your answer.

Do the problems in order in your bluebook. Show and justify your work.

  1. What is the probability of drawing “a picture card or a heart” from a deck of cards?
  2. A person playing the new casino game “Math-Casino” has odds of 123 to 2 against winning. What is the probability of of winning playing this game?
  3. Youroll 2 dice. What is the probability that the total on the two dice is at least ten given that it is even?
  4. Youflip a coin three times. Find the probability of getting three heads given that you get at least two heads.
  5. The local Math store hires youas a salesman. Youare told that youwill receive a commissions. The commission will be $100 with probability 0.73, or $1000 with probability 0 .17, or $5000 with probability 0.10. What is your expected commission?
  6. You pay a dollar and roll two dice. If the sum is at least nine you’re paid four dollars (for a net gain of three). Otherwise you’re paid nothing. What is the expected value of playing this game?
  7. Spacely Sprockets buys 48% of its materials from Mobile, 27% from Pensacola, and the rest from Biloxi. Of these materials, 6% of those from Mobile are substandard, 11% of those from Pensacola are substandard, and 9% of those from Biloxi are substandard. Are the events “materials purchased are substandard” and “materials purchased are not from Alabama” independent?
  8. Youflip a coin three times. Determine whether or not the events “the first two tosses are heads” and “the third toss is a head” are independent.

Spring 99 Math 110 Final Exam Prof. Brick

Do the problems in order in your bluebook. Show and justify your work.

  1. Use a Venn diagram to determine whether the following is a valid syllogism: Math classes are fun. This class is a math class. Therefore, this class is fun.
  2. Use a truth table to determine whether or not the wffs (¬p) → q and p∨q are equivalent.
  3. From a group of eleven men and six women, you wish to form a committee of four men and three women. How many different committees can youform? Explain your answer.
  4. What is the probability of getting a full house (a three-of-a-kind and a pair) when you draw five cards from a deck of cards?
  5. Youflip a coin three times. Find the probability of getting at least two heads.
  6. You pay a dollar and roll two dice. If the sum is at least ten you’re paid three dollars (for a net gain of two). Otherwise you’re paid nothing. What is the expected value of playing this game?
  7. Youflip a coin three times. Determine whether or not the events “the first two tosses are tails” and “the third toss is a head” are independent.
  8. A data set has a frequency histogram with four bars, one at x = 2 with height 5, another at x = 7 with height 3, another at x = 9 with height 1, and one at x = 10 with height 1. Find the mean and standard deviation of the data set.
  9. Market research shows that each year 60% of people who drink 6-up keep drinking 6-up, while the rest switch to Sprout. And 70% of those who drink Sprout keep drinking Sprout, with the remainder switching to 6-up. Find the transition matrix. Suppose initially everyone drinks Sprout. What will the market breakdown be two years later? (Be sure to label which percentage is which.)
  10. The amount of time between taking the decongestant Sideffect and getting relief is normally distributed with a mean of 25 minutes and a standard deviation of 5 minutes. Find the probability that the time between taking Sideffect and getting relief is between 20 and 35 minutes.