Let A be a subset of the set {1,2,...,n}. The number of elements of A is r, 1<=r<=n (|A| = r). What is the probability that A does not contain any consecutive elements?
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Let A be a subset of the set {1,2,...,n}. The number of elements of A is r, 1<=r<=n (|A| = r). What is the
Given information:
Let A be a subset of the set . The number of elements of A is r, .
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- A poker hand consisting of 9 cards is dealt from a standard deck of 52 cards. Find the probability that the hand contains exactly 7 face cards. Leave your answer as a reduced fraction. The probability is | Enter a reduced fraction or integer (no mixed numbers) [more..]answer asapLet A and B be events. Assume that P(A) = 0.55, P(B|A) = 0.36, and P(B|A') = 0.84. Then, P(A∩B)=?, P(B)=?, P(A|B)=?.
- A class contains 40 students. The probability of failing in one of the courses for each student is 0.03, but there is no chance to fail in more than one course. You know that a student failed in a course, the probability that the fail reason in non-attendance is 0.04. All other fail reasons are low average. The examinations are private, so the results are mutually independent. Let X and Y be the numbers of failed students due to non-attendance and due to low average, respectively, in that class this semester. Find the joint MGFSuppose that 80% of American homes have a microwave oven. Let X be the number of American homes in a random sample of n=20 that have a microwave oven. Find the probability that X is at most 18 and at least 16.I’m taking a probability and statistics class please get this correct because I’ve gotten wrong answers before
- There are 2 players in a game. Each player independently picks a real number on the interval [0, 1] uniformly. If the (absolute) difference between the two numbers is less than a (0 < a < 1) and the sum of the two numbers is less than 1, then both players win, otherwise both players lose. What is the probability of winning? 2.The probability that a person owns a car is 0.85, that a person owns a laptop is 0.45, and that a person owns both a car and a laptop is 0.35. If a person is selected at random, a) Find the probability that the person owns either a car or a laptop. b) Find the probability that the person has a laptop given that he has a car also. c) Find the probability that the person has neither a car nor a laptop. d) Show that the events 'own a car' and 'own a laptop' are not independent.Let n be a positive integer. Suppose you have n objects and n buckets. For each object, randomly place it into a bucket, with each of thenoptions being equally likely. Through this random process, some buckets may end up empty, while other buckets may have mul-tiple objects. For each integer k with 0≤ k ≤n, define pn(k) to be the probability that a randomly chosen bucket contains exactly k objects. By definition, pn(0) +pn(1) +pn(2) +. . .+pn(n−1) +pn(n) = 1. Question: As n→ ∞, determine the exact values (or “limits”) for the probabilities pn(0), pn(1), pn(2), pn(3). Clearly show all of your steps and calculations. Use these results to show that when n is sufficiently large, over 98% of the buckets contain atmost three elements. (This explains why Bucket Sort is such an effective sorting algorithm.)
- Solve a,bA diagnostic test for a certain disease is applied to n individuals known to not have the disease. Let X = the number among the n test results that are positive (indicating presence of the disease, so X is the number of false positives) and p = the probability that a disease-free individual's test result is positive (i.e., p is the true proportion of test results from disease-free individuals that are positive). Assume that only X is available rather than the actual sequence of test results. (a) Derive the maximum likelihood estimator of p. p = If n = 20 and x = 7, what is the estimate? p = (b) Is the estimator of part (a) unbiased? Yes O No (c) If n = 20 and x = 7, what is the mle of the probability (1 - p)5 that none of the next five tests done on disease-free individuals are positive? (Round your answer to four decimal places.) Need Help? Read It
