1- Let a coin and a die be tossed; let the sample space S consists of the twelveelements:S-{HI, H2, НЗ, Н4, Н5, Н6, Т1, Т2, ТЗ, Т4, Т5, T6}(i) Express explicitly the following events:A={heads and an even number appear}B={a prime number appears}C={tails and an odd number appear}(ii) Express-explicitly the event-that:(a) A or B occurs.(b) Band C occurs(c) Only Boccurs.(iii) which of the events A, B and C are mutually exclusive?iii onlySelect one:О а. В and CO b. A and BO C. A and B and CO d. A and C

Given: Sample space is shown below S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6} A = heads…

Answered: Let a coin and a die be tossed; let the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Fifty boxes labeled with numbers from 1 to 50 are laid on a table. In each box there is a blue ball and a red ball. From each box that you randomly choose, you pick only one ball randomly, without looking into the box. Right after a ball is picked up, its corresponding box is moved away from the table to avoid picking the same box again. You continue this process until 25 boxes are chosen. 1) What is the probability of picking 8 blue balls and 17 red balls from boxes with even numbered labels? If accidentally you see the fifth ball after being picked up to be Red, what would be the probability of picking 8 blue balls mentioned as above?
Consider a collection of envelopes consisting of one red envelope, three blue envelopes, two green envelope, and two yellow envelope if one of the envelopes is selected at random, determine the probability that a green or a yellow envelope is selected
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In an international school, there are two foreign language courses, German and French. Each student must enroll one and only one of the two courses. According to the students' preferences survey conducted at the induction day, 60% of students decide to study German. Suppose now there are 7 students in the registration counter. (а) What is the probability that among the 7 students, all students will enroll in German course? (b) What is the probability that among the 7 students, there will be more enrollments in French course than German course? (c) For many groups, each with 7 students, find the expectation and standard deviation of the number of students will enroll in German course in a group.
Suppose in a class there are 170 students. Of those 170 students, 90 are males and 80 are females. Among 90 male students, 55 like playing the game of football and 35 do not like it. Among 80 female students, 10 like playing the game of football and 70 do not like it. Represent all this information in the form of a cross tabulation or probability contingency table. Show probability tree diagrams for all the possible random events that can occur (with their probabilities) if a student is picked randomly.
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Find the number of ways in which all twelve letters of the word MISSPELLINGS can be arranged if both the I's are placed at the beginning and both the L's are placed at the end, between any two S's, there must be at least 4 other letters. A group of 8 letters is randomly selected from the letters of the word MISSPELLINGS. Find the probability that (iii) all 8 letters are distinct, (iv) the 2 I's are next to each other, the 2 L's are next to each other, and the 3 S's are next to each other.
Discrete Probability: A bag contains 8 red, 7 green, 5 black and 10 yellow jellybeans. Six jellybeans are selected at random without replacement. a) What is the probability that at least one of the jellybeans is yellow? b) What is the expected number of black jellybeans to be selected?
12 - In a communication channel, data are sent in 10-bit packets. The percentage of a bit sent with error on this channel is 5% and the errors are independent from each other. What is the probability that there is exactly one bad bit in a packet sent over this channel.A) 0.3151B) 0.279C) 0.0746D) 0.0105E) 0.5987
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