1. How are permutations different from combinations? 2. Suppose there are 365 days in a year and we are ignoring leap years. Suppose there are n property owners’ club of which you are not a member. You can only become a member if the registration date of your property matches with that of any of the n owners.
a. What is the probability of this match (in terms of n)? Hint: find the probability of the complement event. b. What should n be for chances of the match being 50%? Why may this number be different from 365/2?
c. Suppose they refuse you a membership in the club. For you to challenge them, you need to show that none of the n existing owners have their registration on the same day. What is the probability of this happening? You may leave the answer as an expression, instead of a number. 3. An insurance company finds that Mark has a 8% chance of getting into a car accident in the next year. If Mark has any kind of accident then the company guarantees to pay him $10, 000. The company has decided to charge Mark a $200 premium for this one year insurance policy.
a. Let X be the amount of profit or loss from this insurance policy in the next year for the insurance company. Find EX, the expected return for the Insurance company? Should the insurance company charge more or less on its premium? b. What amount should the insurance company charge Mark in order to guarantee an expected return of $100? [10%]
4. Suppose that, some time in the distant future, the average number of burglaries in New York City in a week is 2.2. Approximate the probability that there will be a. no burglaries in the next week;
b. at least 2 burglaries in the next week. 5. A NYU student claims that she can distinguish Van Leewen ice cream from Hagen Dazs’s ice cream. There are 60% chance of her claim to be true. a. What is the probability that she needs to test 8 samples to guess the ice cream correctly for the first time. How many ice creams does she need to test on average to arrive at the first correct guess?
b. What is the probability her 8th correct guess comes with the 10th sample that she tastes?
Category: Probability
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Title: Probability and Combinatorics: Exploring Permutations, Combinations, and Expected Returns
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Title: The Pitfalls of Self-Reported Data Collection Self-reported data refers to information that is provided by individuals about themselves, typically through surveys or questionnaires. This type of data collection is often used in research studies, market research,
Explain why using self-reported data instead of measured data is a potential pitfall in data collection. Be sure to include an example.
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“Probability of Drawing Two Specific Colored Marbles from a Bag without Replacement”
“Suppose you have a bag containing 5 red marbles, 3 blue marbles, and 2 green marbles. You randomly select two marbles from the bag without replacement. What is the probability that the first marble drawn is red and the second marble drawn is blue?”
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“Understanding Data Analysis and Sampling Techniques: Exploring ESP, Critical Thinking, and Measurement”
Instructions
This Discussion Board requires you to answer four questions. For each question, do not simply provide an answer; make sure you explain how you arrived at that answer. Please see the corresponding grading rubric to see how each question is assessed. This is an opportunity for you to show your knowledge and understanding of the weekly concepts. You are strongly encouraged to respond to your classmates’ posts with positive and meaningful feedback and will receive up to one point extra credit per discussion board if you do so. This is meant to be a place where we can learn from one another in an engaging and supportive way! Questions
1. ESP: For several years, the U.S. General Social Survey asked subjects, “How often have you felt as though you were felt you were in touch with or connected with someone when they were far away from you?” Of 3887 sampled subjects who had an opinion, 1407 said never and 2480 said at least once. a. Describe the population of interest.
b. Calculate the descriptive statistics (sample proportions).
c. What is the population parameter we want to draw conclusions about (make an inference about)? 2. Use critical thinking to develop an alternative conclusion. A study shows that the number of reported sexually transmitted diseases was significantly higher for high schools that offered courses in sex education than for high schools that did not. Conclusion: The introduction of sex education courses at the high school level has resulted in increased promiscuity among teens. 3. An engineer is designing a machine to manufacture gloves and she obtains the following sample of hand lengths (mm) of randomly selected adult males based on data gathered:
173 179 207 158 196 195 214 199
a. Define this data set as discrete or continuous. b. Hand lengths are what type of level of measurement? c. Compare the mean and median for this data set and if you can draw any conclusions from these values. 4. Explain the difference between stratified and cluster sampling. Why do you think that cluster sampling is frequently used in practice?