(5) Suppose that I go on choosing numbers uniformly at random, independently fromthe set {1, 2, .., 100}. What is the expected number of trials I will need to obtain30 distinct numbers?.....

A random variable is a variable whose values depend on outcomes of a random event. Also called…

Answered: (5) Suppose that I go on choosing…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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9 A bag contains 12 red and 8 blue balls that are identical except for their colour. A ball is chosen from the bag, its colour noted, and then it is replaced. Eight balls are chosen. (i) Find (a) the probability of obtaining five red balls (b) the probability of obtaining at least two blue balls (c) the probability of obtaining equal numbers of red and blue balls. (ii) How many balls need to be chosen if the probability of obtaining at least one red ball is to be at least 99%?
0. A box has 10 coins of which, 6 coins are fair, 4 coins are loaded such that the probability of getting a tail is 1/3 with each loaded coin. A coin is selected from the box at random and is tossed once with the result of tail. Find the conditional probability that the coin is fair.
84. (a) If for two events, A and B 1 Then find P(BA). 4 P(B) = and P(A/B) = 2 (b) If P(A) = 0.4, P(A U B) = 0.7, then, for two independent events, A and B, find P (B). (c) One of the two events, A and B, must occur. If the chance if 4 is of that of B, then find 3 odds in favour of B. (d) In an examination, 50% and 40% students failed in mathematics and statistics, respectively, and 20% failed in both the subjects. A student is selected at random, find the probability that, (i) The student failed in statistics when it is known that he failed in mathematics. (ii) The student failed in exactly one subject
Please help me with this discrete II problem. Thank you
Let S be a sample space and E and F be events associated with S. Suppose that Pr(E) = 0.5, Pr(F) = 0.3 and Pr(ENF) = 0.2. Calculate the following probabilities. (a) Pr(E|F) (b) Pr(F|E) (c) Pr(티F') (d) Pr (E'JF') ... (a) To find Pr(E|F), simplify the fraction with Pr(EnF) in the numerator and Pr(F) in the denominator. Pr(E|F) = || |(Type an integer or a simplified fraction.)
6. Someone plans to travel at the weekend. According to the weather forecast, the probability of raining on the first and the second day of weekends is 0.5 and 0.3 respectively, the probability of raining on both days is 0.2. Try to find: (Let Ai be event of raining on the ith day, i = 1,2, then P (A₁) = 0.5, P (A2) = 0.3, P (A1 A2) = 0.2.) (1) The probability of raining on the first day but not on the second day; (2) The probability of raining on one of the two days; (3) The probability of raining at least on one day.
5. a) Suppose you have three coins in a bag: the first coin is fair, with prob- ability of HEAD (H) equals to that of TAIL (T), i.e., P(X = H|M1) = P(X = T|M1), where X is a binary random variable representing HEAD or TAIL. The second is a loaded coin with P(X = takes a coin out of the bag at random and flips it. When it lands, you observe that the side of the coin facing up is HEAD. What is the probabilities that this is the first, second and third coin? Hint: You may assume the three coins are equal likely to be selected from the bag, i.e., P(M1) = P(M2) = P(M3) = , and you need to calculate P(M||X = H), P(M2|X = H) and P(M3|X = H). H|M2) = 0.8. The third is also a loaded coin with P(X = Н Мз) — 0.2. Your friend 6) What if we don't know the probabilities of HEAD for each coin? Design an iterative algorithm using pseudo-code to estimate these probabilities.
2. A student majoring in phycology is trying to decide on the number of firms to which he should apply. Given his work experience and grades he can expect to receive a job offer from 75% of the firms he applies. The student decides to apply to only 4 firms. What is the probability that he receives?a) No job offers P(x = 0) b) Less than 2 job offers P(x <2) c) At least 2 job offers P(x ≥ 2)
What is the likelihood of selecting a 4-digit number in the win-4 lottery, where one digit appears exactly three times, given that each digit from 0 to 9 has an equal probability of being drawn in each of the four draws? Note that the number starts with 0 is a valid 4 digit-number such as 0001 is an option

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(5) Suppose that I go on choosing numbers uniformly at random, independently from the set {1,2, .., 100}. What is the expected number of trials I will need to obtain 30 distinct numbers? .....T