7. If 2n boys are divided into two equal subgroups find the probability that the twO tallest boys will be (a) in different subgroups and (b) in the same subgroup. 8. In a movie theater that can accommodate n+k people, n people are seated. What is the probability that r n given seats are occupied? 9. Waiting in line for a Saturday morning movie show are 2n children. Tickets are priced at a quarter each. Find the probability that nobody will have to wait for change if, before a ticket is sold to the first customer, the cashier has 2k (k < n) quarters. Assume that it is equally likely that each ticket is paid for with a quarter or a half- dollar coin 0. Each box of a certain brand of breakfast cereal contains a small charm, with k distinct charms forming a set. Assuming that the chance of drawing any particular charm is equal to that of drawing any other charm, show that the probability of finding at least one complete set of charms in a random purchase of N k boxes equals 1 OMBINATORICS: PROBABILITY ON FINITE SAMPLE SPACES m 1- k 1N N k k- 2 -0E k k-3 N + k 2 k 3 k N ++-1)0-(1) (E) k IAS k - 1 /DIN [Hint: Use (1.3.6).] idi .Prove Rules 1-4. - In a five-card poker game, find the probability that a hand will have: (a) A royal flush (ace, king, queen, jack, and 10 of the same suit). (b)A straight flush (five cards ina sequence, all of the same suit; ace is 2, 3, 4, 5 is also a sequence) excluding a royal flush.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Transcribed Image Text:7. If 2n boys are divided into two equal subgroups find the probability that the twO tallest boys will be (a) in different subgroups and (b) in the same subgroup. 8. In a movie theater that can accommodate n+k people, n people are seated. What is the probability that r n given seats are occupied? 9. Waiting in line for a Saturday morning movie show are 2n children. Tickets are priced at a quarter each. Find the probability that nobody will have to wait for change if, before a ticket is sold to the first customer, the cashier has 2k (k < n) quarters. Assume that it is equally likely that each ticket is paid for with a quarter or a half- dollar coin 0. Each box of a certain brand of breakfast cereal contains a small charm, with k distinct charms forming a set. Assuming that the chance of drawing any particular charm is equal to that of drawing any other charm, show that the probability of finding at least one complete set of charms in a random purchase of N k boxes equals