In question 4 you may use any of the 10 rules of probability theory we have derived to solve the following problems. For each problem, specify the sample space S, specify the event using E or F (with or without subscripts) and make sure you cite the rule you're using in each step of your solution. In question 4 you may use any of the 10 rules of probability theory we have derived to solve the followingproblems. For each problem, specify the sample space S, specify the event using E or F (with or withoutsubscripts) and make sure you cite the rule you're using in cach step of your solution.(a) In a box there are 2 white, 3 black, and 4 red balls. If a ball is drawn at random, what is the probabilitythat it is black? That it is not red?(b) A single card is drawn at random from a shuffled deck. What is the probability that it is red? That itis the ace of hearts? That is either a three or a five? That it is either an ace or red or both? (c) A letter is selected at random from the alphabet. What is the probability that is one of the letters inthe word 'probability"? What is the probability that it occurs in the first half of the alphabet? What isthe probability that it is a letter after r?(d) You are going shopping this weekend at the local mall. Suppose that the mall you go to has fourentrances, one on the North, one on the South, and two on the East. If you enter at random, shop andthen exit at random, what is the probability that you enter and exit on the same side of the mall?

As per policy I have calculated first main question as you have posted multiple questions, plz…

Answered: (a) In a box there are 2 white, 3…

(a) In a box there are 2 white, 3 black, and 4 red balls. If a ball is drawn at random, what is the probability that it is black? That it is not red?

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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Question

In question 4 you may use any of the 10 rules of probability theory we have derived to solve the following problems. For each problem, specify the sample space S, specify the event using E or F (with or without subscripts) and make sure you cite the rule you're using in each step of your solution.

(c) A letter is selected at random from the alphabet. What is the probability that is one of the letters in
the word 'probability"? What is the probability that it occurs in the first half of the alphabet? What is
the probability that it is a letter after r?
(d) You are going shopping this weekend at the local mall. Suppose that the mall you go to has four
entrances, one on the North, one on the South, and two on the East. If you enter at random, shop and
then exit at random, what is the probability that you enter and exit on the same side of the mall?

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