Suppose that 5 of the numbers 1, 2, . . . , 14 are chosen. Find...
Suppose that 5 of the numbers 1, 2, . . . , 14 are chosen. Find the probability that 9 is the third smallest value chosen.
Homework Answers
the probability that 9 is the third smallest value chosen Suppose that 5 of the numbers 1, 2, . . . , 14 are chosen.= 8c2*5c2/14c5=0.2797
(FP.11) From the set {1, 2, ..., 15} four numbers have been randomly chosen. Find the...
(FP.11) From the set {1, 2, ..., 15} four numbers have been randomly chosen. Find the probability of the events that (a) The smallest chosen number is 6. (b) The smallest chosen number is 6 and the largest is 14. (c) All the chosen numbers are odd.
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)...
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 1 (35 points): Two numbers are chosen at random and simultaneously from among the numbers...
Problem 1 (35 points): Two numbers are chosen at random and simultaneously from among the numbers 1 to 4 without replacement. Let A,产(1,2,3,41, be the event that the first number is . 1. Find the probability of the event B that the second number chosen is 3. 2. What is the probability that the first number is 1 given that the second number is 3?
Suppose 6 numbers are generated by a computer, each uniform on the interval (0, 1). Let...
Suppose 6 numbers are generated by a computer, each uniform on the interval (0, 1). Let Y be the random variable representing the smallest of the numbers. (a) Show that the probability density of Y is given by py (t) -61-t)5, 0t <1 [51 Hint: The probability density for the r-th largest random variable can be derived using the Beta distribution by letting a = r and ?-n-r +1. (b) What is the probability that the smallest number is less...
In a lottery game, a player picks 4 numbers from 1 to 46. If 2 of...
In a lottery game, a player picks 4 numbers from 1 to 46. If 2 of those 4 numbers match those drawn, the player wins third prize. Let's walk through the steps to determine the probability of winning third prize. In how many ways can 2 winning numbers be chosen from the possible 4 numbers? In how many ways can 2 non-winning numbers be chosen from the pool of all non-winning numbers? The number of favorable outcomes would be to...
Given a matrix with m rows and n columns, m adjacent numbers are chosen from m...
Given a matrix with m rows and n columns, m adjacent numbers are chosen from m rows, where two numbers are adjacent to each other if they are directly connected vertically or diagonally and only one number is taken from one row. Design a dynamic programming algorithm to find the smallest sum of these m numbers. For example, given a 3 by 3 matrix 1 2 3 4 5 6 7 0 2 The sum of three numbers 1, 4,...
2. In the Texas Pick-6, six numbers are chosen (without repetition) from 1 through 54 and...
2. In the Texas Pick-6, six numbers are chosen (without repetition) from 1 through 54 and the order does not matter. You win the grand prize if you get all six numbers right. (a.) How many possible tickets are there? What is the probability of winning the grand prize? (b.) You win $1,595 if you pick 5 out of 6 correct numbers. What is the probability of winning $1,5952 (c.) You lose if you get fewer than 3 numbers correct....
Suppose that X is uniformly selected from the numbers 1, 2, 3 (that is, P(X =...
Suppose that X is uniformly selected from the numbers
1, 2, 3 (that is, P(X = i) = 1/3 for
i = 1, 2, or 3). Once X is selected, Y is chosen uniformly from the
numbers 0, 1, ..., X. Find
E[X | Y ].
(c) Compute EX Y 7. Suppose that X is uniformly selected from the numbers 1, 2, 3 (that is, P(X- i) 1/3 for ,X. Find i = 1,2, or 3). Once X is selected,...
(FP.11) From the set {1, 2, ..., 15} four numbers have been randomly chosen. Find the probability of the events that (a) The smallest chosen number is 6. (b) The smallest chosen number is 6 and the largest is 14. (c) All the chosen numbers are odd.
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)...
Problem 1 (35 points): Two numbers are chosen at random and simultaneously from among the numbers 1 to 4 without replacement. Let A,产(1,2,3,41, be the event that the first number is . 1. Find the probability of the event B that the second number chosen is 3. 2. What is the probability that the first number is 1 given that the second number is 3?
Suppose 6 numbers are generated by a computer, each uniform on the interval (0, 1). Let Y be the random variable representing the smallest of the numbers. (a) Show that the probability density of Y is given by py (t) -61-t)5, 0t <1 [51 Hint: The probability density for the r-th largest random variable can be derived using the Beta distribution by letting a = r and ?-n-r +1. (b) What is the probability that the smallest number is less...
2. In the Texas Pick-6, six numbers are chosen (without repetition) from 1 through 54 and the order does not matter. You win the grand prize if you get all six numbers right. (a.) How many possible tickets are there? What is the probability of winning the grand prize? (b.) You win $1,595 if you pick 5 out of 6 correct numbers. What is the probability of winning $1,5952 (c.) You lose if you get fewer than 3 numbers correct....
Suppose that X is uniformly selected from the numbers
1, 2, 3 (that is, P(X = i) = 1/3 for
i = 1, 2, or 3). Once X is selected, Y is chosen uniformly from the
numbers 0, 1, ..., X. Find
E[X | Y ].
(c) Compute EX Y 7. Suppose that X is uniformly selected from the numbers 1, 2, 3 (that is, P(X- i) 1/3 for ,X. Find i = 1,2, or 3). Once X is selected,...
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