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An experiment consists of tossing a fair die until a 6

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 205SE Chapter 3

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 205SE

Problem 205SE

An experiment consists of tossing a fair die until a 6 occurs four times. What is the probability that the process ends after exactly ten tosses with a 6 occurring on the ninth and tenth tosses?

Step-by-Step Solution:

Answer:

Step 1 of 1:

An experiment consists of tossing a fair die until a six occurs 4 times.

We need to find the probability that the process ends after exactly 10 tosses with a six occurring on the 9th and 10th tosses.

Sample space of fair die

Hence, from the sample space the probability of occurrence of six,

According to the question, out of 4 times in 10 tosses, six occurs exactly in ninth and tenth tosses and other two six can occur in any of first 8 tosses.

Hence first two six occurs in any of first 8 tosses is random and hence follows the binomial distribution with parameter

Let represent the number of tosses till first two sixes occur.

A random variable  is said to have a binomial probability distribution based on  trials with success probability  if and only if

………….(1)

……..(1)

The probability of getting sixes on the 9th and 10th tosses,

 ………(2)

Therefore the required probability using equation (1) and (2),

Hence the probability that the process ends after exactly 10 tosses with a six occurring on the 9th and 10th tosses is


Step 2 of 1

Chapter 3, Problem 205SE is Solved
Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. Since the solution to 205SE from 3 chapter was answered, more than 469 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 205SE from chapter: 3 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM. This full solution covers the following key subjects: tosses, occurring, ends, exactly, experiment. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. The answer to “An experiment consists of tossing a fair die until a 6 occurs four times. What is the probability that the process ends after exactly ten tosses with a 6 occurring on the ninth and tenth tosses?” is broken down into a number of easy to follow steps, and 36 words.

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An experiment consists of tossing a fair die until a 6