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Problem 1 (35 points): Two numbers are chosen at random and simultaneously from among the numbers...
6 numbers are chosen in order from the numbers 1, 2, ..., 49 a. Find the...
6 numbers are chosen in order from the numbers 1, 2, ..., 49 a. Find the probability the numbers are drawn in **strictly** increasing order; (i.e., the first < the second < the third) if i. draws are made without replacement ii. draws are made with replacement. b. Assume the draws are made without replacement. Find the probability that the numbers form an arithmetic sequence drawn in any possible order (for example 9,3,6,12,18,15) C.Assume the draws are made with replacement....
about something, ask! Part .Do any eight (8) of 1-9 1. Two numbers are chosen at...
about something, ask! Part .Do any eight (8) of 1-9 1. Two numbers are chosen at random in succession, with replacement, from the set 1, 2, 3, , 100J. What is the probability that the first one is larger than the second one? [15) 2. In a set of dominoes, each piece is marked with two numbers, one on each end. The pieces are symmetrical, so that the two numbers are unordered. (That is, you can't tell (1,4) and (4,1)...
4.26 In a lottery game, three winning numbers are chosen uniformly at random from (1, ,100), samp...
4.26 In a lottery game, three winning numbers are chosen uniformly at random from (1, ,100), sampling without replacement. Lottery tickets cost $1 and allow a player to pick three numbers. If a player matches the three winning numbers they win the jackpot prize of $1,000. For matching exactly two numbers, they win $15. For matching exactly one number they win $3 d) Hoppe shows that the probability that a single parlayed ticket will ulti- mately win the jackpot is...
5 numbers chosen randomly without replacement. "B" represents number of even numbers, this random variable has...
5 numbers chosen randomly without replacement. "B" represents number of even numbers, this random variable has this probability: x 0 1 2 3 4 5 p(B=x) 0.02693 0.15989 .33858 .31977 .13464 .02020 number of odd #s chosen would then be 5-x, if x is even #s chosen. "C" represents difference b/w # of even and # of odd chosen, --> C= 2B-5 a. probability that exactly 1 even # chosen? b. probability at most 1 even # chosen? c. prob....
Problem 3: If 13 cards are to be chosen at random (without replacement) from an ordinary...
Problem 3: If 13 cards are to be chosen at random (without replacement) from an ordinary deck of 52 cards, find the probability that (a) 6 will be picture cards. (b) None will be picture cards.
2. Suppose an integer is chosen at random from the set S of the first 2510 positive integers that is, from the set S- [...
2. Suppose an integer is chosen at random from the set S of the first 2510 positive integers that is, from the set S- [1,2,3,...,2510). Let A be the event that the number chosen is a multiple of 47. Let B be the event that the number chosen is a multiple of 23. (a) Determine with reason whether the events A and B are mutually exclusive. (b) Determine with reason whether the events A and B are independent (c) Determine...
Part 1 Suppose that 2 batteries are randomly chosen without replacement from a group of 12...
Part 1 Suppose that 2 batteries are randomly chosen without replacement from a group of 12 batteries: 3 new, 4 used (working), and 5 defective. Let the random variable X denote the number of new batteries chosen and the random variable Y denote the number of used batteries chosen. The joint distribution fxy is given in the following table: 0 12 17663/6 120/6612/66 1. Calculate P ( X 1 ,Y > 1) 2. Find the marginal probability mass function fx...
In Lotto 4-39, the lottery picks 4 numbers (without replacement) from 1 to 39. Before this...
In Lotto 4-39, the lottery picks 4 numbers (without replacement) from 1 to 39. Before this drawing is done, you pick 4 numbers (without replacement) from 1 to 39. Find the probability that: a) None of my numbers are chosen B)exactly 2 are chosen For a) I figured out total number of possibilities 39C4, then I did 1/39C4 for the probability because I figured no numbers was just one possible combination. Where did I go wrong?
question1: A company randomly generates 5-digit passwords for its clients. Each contains 3 unique numbers chosen...
question1: A company randomly generates 5-digit passwords for its clients. Each contains 3 unique numbers chosen from {0, 1, ..., 5} & 2 unique letters from {A, ..., G}. Determine the probability that Sally receives a password containing the letters B & E (in either order) & the numbers 2, 4, 5 (in any order). question2: With probability = .25 , two switches are selected without replacement from box A, & with probability = .75 , two switches are selected...
A letter is chosen uniformly at random from {A, B, . . . , Z}. If...
A letter is chosen uniformly at random from {A, B, . . . , Z}. If that letter is one of the vowels (i.e. A, E, I, O or U) then a second letter is chosen uniformly at random from {A, B, . . . , Z}. Let L be the number of letters chosen and let V be the number of vowels chosen. (i) What is the expected value of L? (ii) What is the expected value of V?...
6 numbers are chosen in order from the numbers 1, 2, ..., 49 a. Find the probability the numbers are drawn in **strictly** increasing order; (i.e., the first < the second < the third) if i. draws are made without replacement ii. draws are made with replacement. b. Assume the draws are made without replacement. Find the probability that the numbers form an arithmetic sequence drawn in any possible order (for example 9,3,6,12,18,15) C.Assume the draws are made with replacement....
about something, ask! Part .Do any eight (8) of 1-9 1. Two numbers are chosen at random in succession, with replacement, from the set 1, 2, 3, , 100J. What is the probability that the first one is larger than the second one? [15) 2. In a set of dominoes, each piece is marked with two numbers, one on each end. The pieces are symmetrical, so that the two numbers are unordered. (That is, you can't tell (1,4) and (4,1)...
4.26 In a lottery game, three winning numbers are chosen uniformly at random from (1, ,100), sampling without replacement. Lottery tickets cost $1 and allow a player to pick three numbers. If a player matches the three winning numbers they win the jackpot prize of $1,000. For matching exactly two numbers, they win $15. For matching exactly one number they win $3 d) Hoppe shows that the probability that a single parlayed ticket will ulti- mately win the jackpot is...
Problem 3: If 13 cards are to be chosen at random (without replacement) from an ordinary deck of 52 cards, find the probability that (a) 6 will be picture cards. (b) None will be picture cards.
2. Suppose an integer is chosen at random from the set S of the first 2510 positive integers that is, from the set S- [1,2,3,...,2510). Let A be the event that the number chosen is a multiple of 47. Let B be the event that the number chosen is a multiple of 23. (a) Determine with reason whether the events A and B are mutually exclusive. (b) Determine with reason whether the events A and B are independent (c) Determine...
Part 1 Suppose that 2 batteries are randomly chosen without replacement from a group of 12 batteries: 3 new, 4 used (working), and 5 defective. Let the random variable X denote the number of new batteries chosen and the random variable Y denote the number of used batteries chosen. The joint distribution fxy is given in the following table: 0 12 17663/6 120/6612/66 1. Calculate P ( X 1 ,Y > 1) 2. Find the marginal probability mass function fx...
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