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For the lottery described in Exercise 2.4-13, find the

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 14E Chapter 2.4

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 14E

Problem 14E

For the lottery described in Exercise 2.4-13, find the smallest number of tickets that must be purchased so that the probability of winning at least one prize is greater than (a) 0.50; (b) 0.95.

Reference Exercise 2.4-13

It is claimed that for a particular lottery, 1/10 of the 50 million tickets will win a prize. What is the probability of winning at least one prize if you purchase (a) 10 tickets or (b) 15 tickets?

Step-by-Step Solution:
Step 1 of 3

Solution 14E

Step1 of 3:

We have lottery game in that a particular lottery, 1/10 of the 50 million tickets will win a prize.

That is p =

               = 0.1.

We need to find,

The smallest number of tickets that must be purchased so that the probability of winning at least one prize is greater than (a) 0.50; (b) 0.95.

Step2 of 3:

Let “X” be random variable which follows binomial distribution with parameters n and p.

That is X B(n, p)

The probability mass function of binomial distribution is given below

P(X) = nCx , x = 0,1,2,...,n.

Where,

X = random variable

n = sample size

p = probability of success(or proportion).

a).

Consider,

P(X1) > 0.50

1 - P(X1) > 0.50

1 - P(X = 0) > 0.50

1 - nC0  > 0.50

1 - [1(1)] > 0.50

1 -  > 0.50

1 - 0.50 >

0.50 >

Now we need to solve for n for that take Ln(natural logarithm on both side)

Ln(0.50) > Ln[]

Ln(0.50) > n Ln(0.9)

            n  

          n

          n 6.57634

              n 7

Hence, n7.

Therefore, minimum 7 tickets have to be purchase.


Step3 of 3:

b).

Consider,

P(X1) > 0.95

1 - P(X1) > 0.95

1 - P(X = 0) > 0.95

1 - nC0  > 0.95

1 - [1(1)] > 0.95

1 -  > 0.95

1 - 0.95 >

0.05 >

Now we need to solve for n for that take Ln(natural logarithm on both side)

Ln(0.05) > Ln[]

Ln(0.05) > n Ln(0.9)

            n  

          n

          n 28.4225

            n 29

Hence, n29.

Therefore, minimum 29 tickets have to be purchase.


Conclusion:

Therefore,The smallest number of tickets that must be purchased so that the probability of winning at least one prize is greater than

(a) 0.50 = 7 tickets

(b) 0.95 = 29 tickets.

Step 2 of 3

Chapter 2.4, Problem 14E is Solved
Step 3 of 3

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

The full step-by-step solution to problem: 14E from chapter: 2.4 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. Since the solution to 14E from 2.4 chapter was answered, more than 938 students have viewed the full step-by-step answer. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. The answer to “For the lottery described in Exercise 2.4-13, find the smallest number of tickets that must be purchased so that the probability of winning at least one prize is greater than (a) 0.50; (b) 0.95.Reference Exercise 2.4-13It is claimed that for a particular lottery, 1/10 of the 50 million tickets will win a prize. What is the probability of winning at least one prize if you purchase (a) 10 tickets or (b) 15 tickets?” is broken down into a number of easy to follow steps, and 73 words. This full solution covers the following key subjects: tickets, prize, Probability, exercise, Winning. This expansive textbook survival guide covers 59 chapters, and 1476 solutions.

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