It is claimed that for a particular lottery, 1/10 of the

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

Problem 13E 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 13E

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 13E

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 probability of winning at least one prize if you purchase

(a) 10 tickets or

(b) 15 tickets?

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).

Here we have n = 10 and p = 0.1.

The probability that at least one prize is given by

P(X1) = 1 - P(X1)

              = 1 - P(X = 0)                                ……….(1)

Where,

P(X = 0) = 10C0   [therefore substitute x = 0, n = 10 and p = 0.1 in above pmf]

               = 1(1)(0.3487)

               = 0.3487.

Substitute P(X = 0) = 0.3487 in above equation (1)...

Step 2 of 3

Chapter 2.4, Problem 13E is Solved
Step 3 of 3

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

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