1Permutation notation :2nf (2)f (n),...Choose a random ordering of the symbols 1,2,..,n and use it as the second row.Q1. What is the probability that it is a product of only two disjoint cycles? only n disjoint cycles?

Given permutation is 12…nf1f2…fn. To find the probability, that the permutation is product of two…

Answered: Permutation notation : 2 (n) Choose a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or spades). Complete parts (a) and (b) to obtain the probability of being dealt a flush in five cards. (a) Initially concentrate on one suit, say clubs. There are 13 clubs in a deck. Compute P(five clubs) = P(first card is clubs and second card is clubs and third card is clubs and fourth card is clubs and fifth card is clubs). P(five clubs) = (Round to six decimal places as needed.)
3 of 18 (0 comple You randomly select one card from a 52-card deck. Find the probability of selecting an ace or a five. The probability is (Type an integer or a fraction. Simplify your answer.) Enter your answer in the answer box. Hi C Type here to search
Only answer D and E The probability is 0.4 that the final exam is difficult. If the final exam is difficult, the probability is 0.3 that Nancy will pass the course. If the final exam is not difficult, the probability is 0.9 that Nancy will pass the course. (A) What is the probability that the final exam is not difficult? (B) What is the probability that the final exam is difficult AND Nancy will pass the course? [Use the multiplication rule.] (C) What is the probability that the final exam is not difficult AND Nancy will pass the course? [Use the multiplication rule.] D) What is the probability that Nancy will pass the course? [Use additivity from (B) and (C).] (E) Given the observation that Nancy passed the course, what is the probability that the final exam was difficult? [Use Bayes’ Theorem.]
Hint: Use Principle of Inclusion-Exclusion in probability
13) The integer n = a) If n = 3 (mod 9), then what is x ? b) If n = 3 (mod 11), then what is x ? Hint for #13: 12700140x3243243 is missing the digit x. Consider the number 1234. By writing each digit in scientific notation, we have 1234 1 x 10³ +2× 10² +3 × 10¹ + 4 × 10⁰ Then notice that 10 = 1 (mod 9). When we reduce mod 9, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x 1³ + 2 x 1² + 3 × 1¹ + 4 × 1⁰ = 1+ 2+ 3+ 4 = 10 = 1 (mod 9). Since 10 = -1 (mod 11), when we reduce mod 11, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x (-1)³ +2× (-1)² +3 × (-1)¹ +4× (-1)⁰ = -1 + 2-3 + 4 = 2 (mod 11).
Q 4[ 15M] A box contains 23 products of type A and 44 products of type B. A product is drawn at random from the box. Find the probability that the product drawn is : (i) type A. (ii) type B. (4 decimal places).
A5
Solve Q7
2:51 A flush in the card game of poker occurs if a player gets five cards that are all the same suit (clubs, diamonds, hearts, or spades). Complete parts (a) and (b) to obtain the probability of being dealt a flush in five cards. (a) Initially concentrate on one suit, say clubs. There are 13 clubs in a deck. Compute P(five clubs) = P(first card is clubs and second card is clubs and third card is clubs and fourth card is clubs and fifth card is clubs). P(five clubs) = 0.000495 (Round to six decimal places as needed.) (b) A flush can occur if a player receives five clubs or five diamonds or five hearts or five spades. Compute P(five clubs or five diamonds or five hearts or five spades). Note that the events are mutually exclusive. P(five clubs or five diamonds or five hearts or five spades) = (Round to three decimal places as needed.) Vo) 1 LTE 4G 1% ||| = O
(3 points.) A bag of k∙n marbles contains n marbles of each of k distinct colors. A random sample (without replacement) of k marbles is drawn. Give an expression for Pk,n, defined as the probability the sample contains exactly two colors. Hint: there are (2) possible pairs of colors, and for each color there are (2²7) samples drawn from at most two colors, and this includes 2 (2) samples drawn exclusively from one or the other of the two colors, and of course there are (n) samples overall.
The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through k (d). Males Females Total Nursing majors 93 700 793 Non-nursing majors 1015 1723 2738 Part 3 of 4 Total 1108 2423 3531 P(not being female or being a nursing major) = (Round to the nearest thousandth as needed.). (a) Find the probability that the student is male or a nursing major. P(being male or being nursing major) = 0.512 (Round to the nearest thousandth as needed.) (b) Find the probability that the student is female or not a nursing major. D P(being female or not being a nursing major) = 0.974 (Round to the nearest thousandth as needed.) (c) Find the probability that the student is not female or a nursing major. H C n 101 √₁ Vi L (0,0) 4 x

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Permutation notation : 2 (n) Choose a random ordering of the symbols 1,2,..,n and use it as the second row. ... n f(2) ... Q1. What is the probability that it is a product of only two disjoint cycles? only n disjoint cycles?