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5. One shuffles at random the letters in RAZZMATAZZ. Find the probability that the new word...
(5 p) Two ants move along a rectangular mesh at a pace of 1 block per...
(5 p) Two ants move along a rectangular mesh at a pace of 1 block per timeslice. The two ants start towards each other simultaneously, one from the origin, and the other from (12, 14). They bump into each other after 13 timeslices, earliest possible, at (7, 6). In how many different ways can that happen? 3. (Bump in Manhattan, X blocks East, Y blocks North) (5 p) 5. One shuffles at random the letters in RAZZMATAZZ. Find the probability...
2.12 A permutation of the word "white" is chosen at random. Find the probability that it...
2.12 A permutation of the word "white" is chosen at random. Find the probability that it begins with a vowel. Also, find the probability that it ends with a consonant, and the probability that it begins with a vowel and ends with a consonant.
Exercise 2.38. We choose one of the words in the following sentence uniformly at random and then choose one of the...
Exercise 2.38. We choose one of the words in the following sentence uniformly at random and then choose one of the letters of that word, again uniformly at random: SOME DOGS ARE BROWN (a) Find the probability that the chosen letter is R. (b) Let X denote the length of the chosen word. Determine the probability mass function of X. (c) For each possible value k of X determine the conditional probability P(X k|X 3) Hint. The decomposition idea works...
5. Tiles spelling the word “Restaurant” are placed on a sign above a building. If one...
5. Tiles spelling the word “Restaurant” are placed on a sign above a building. If one of the letters falls down at random, what is the probability that the letter is not a vowel? (JUSTIFY)
7. (a) Find the number of arrangement of the letters in the word DIFFERENTIAL 2 marks] (i) In one...
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7. (a) Find the number of arrangement of the letters in the word DIFFERENTIAL 2 marks] (i) In one selection session, how many ways to choose 11 football players from 2 marks] (b) 20 players? (ii) How many ways to choose one player for goalkeeper, four defenders, four midfielders and two attackers from the 11 players chosen? 2 marks] (iii) How many ways to arrange five players in the first row and the goalkeeper...
COUNTING TECHNIQUES: PROBABILITY AND STATISTICS 3. The word FACETIOUS is one of the only words in...
COUNTING TECHNIQUES: PROBABILITY AND STATISTICS
3. The word FACETIOUS is one of the only words in the English language to contain all five vowels in alphabetical order. If these nine letters are arranged randomly, what is the probability that the resulting"word" also contains the five vowels in order?
Five cheer-leaders for a certain egomaniac are given tee-shirts labelled with one of the letters M,P,U,R.T...
Five cheer-leaders for a certain egomaniac are given tee-shirts labelled with one of the letters M,P,U,R.T and file on stage. They are confused and line up in a random order to form a word. (a) What is the sample space? You need not write out all of the elements of the space, but indicate how many there are and show some pattern for writing them out. (b) Find the probability that the first letter is T, the middle letter is...
Y V1 - X2 Find the probability density for the new random variable Y 3v Abu Nawas is a waiter who...
Y V1 - X2 Find the probability density for the new random variable Y 3v Abu Nawas is a waiter who breaks an average of one dish every two hours. What is the probability that he will break at least one dish in three hours? 4 The x and y coordinates are uniformly distributed over the unit disc x2 + y2 1. Calculate P (Y > X ,
Y V1 - X2 Find the probability density for the new random...
The digit 1, 2, ..., n(n > 5) are put at random in a row. (a)...
The digit 1, 2, ..., n(n > 5) are put at random in a row. (a) Show that the probability that the digits 4 and 5 will be adjacent is 2/n. (b) Find the probability that the digits 4 and 5 will not be adjacent. (c) Find the probability that the digits 4 and 5 will be adjacent or the digits 2 and 3 will be adjacent. That is, find P((4 and 5 adjacent) ∪ (2 and 3 adjacent)).
1. A password of length 5 is generated at random as a sequence of letters from...
1. A password of length 5 is generated at random as a sequence of letters from A,...,Z with repetitions allowed. What is the probability that in every pair of adjacent positions in the password, the letters are different (for example, XJXTQ but not XXJTQ) ? 2. Bowl #1 contains 2 red chips and 3 white chips. Bowl #2 contains 3 red chips and 4 white chips. One of the bowls is chosen at random, and a chip is withdrawn from...
(5 p) Two ants move along a rectangular mesh at a pace of 1 block per timeslice. The two ants start towards each other simultaneously, one from the origin, and the other from (12, 14). They bump into each other after 13 timeslices, earliest possible, at (7, 6). In how many different ways can that happen? 3. (Bump in Manhattan, X blocks East, Y blocks North) (5 p) 5. One shuffles at random the letters in RAZZMATAZZ. Find the probability...
2.12 A permutation of the word "white" is chosen at random. Find the probability that it begins with a vowel. Also, find the probability that it ends with a consonant, and the probability that it begins with a vowel and ends with a consonant.
Exercise 2.38. We choose one of the words in the following sentence uniformly at random and then choose one of the letters of that word, again uniformly at random: SOME DOGS ARE BROWN (a) Find the probability that the chosen letter is R. (b) Let X denote the length of the chosen word. Determine the probability mass function of X. (c) For each possible value k of X determine the conditional probability P(X k|X 3) Hint. The decomposition idea works...
Help me solve this question asap
7. (a) Find the number of arrangement of the letters in the word DIFFERENTIAL 2 marks] (i) In one selection session, how many ways to choose 11 football players from 2 marks] (b) 20 players? (ii) How many ways to choose one player for goalkeeper, four defenders, four midfielders and two attackers from the 11 players chosen? 2 marks] (iii) How many ways to arrange five players in the first row and the goalkeeper...
COUNTING TECHNIQUES: PROBABILITY AND STATISTICS
3. The word FACETIOUS is one of the only words in the English language to contain all five vowels in alphabetical order. If these nine letters are arranged randomly, what is the probability that the resulting"word" also contains the five vowels in order?
Y V1 - X2 Find the probability density for the new random variable Y 3v Abu Nawas is a waiter who breaks an average of one dish every two hours. What is the probability that he will break at least one dish in three hours? 4 The x and y coordinates are uniformly distributed over the unit disc x2 + y2 1. Calculate P (Y > X ,
Y V1 - X2 Find the probability density for the new random...
1. A password of length 5 is generated at random as a sequence of letters from A,...,Z with repetitions allowed. What is the probability that in every pair of adjacent positions in the password, the letters are different (for example, XJXTQ but not XXJTQ) ? 2. Bowl #1 contains 2 red chips and 3 white chips. Bowl #2 contains 3 red chips and 4 white chips. One of the bowls is chosen at random, and a chip is withdrawn from...
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