/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q18E A wallet contains five \(10 bill... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q18E (page 65)

A wallet contains five \(10 bills, four \)5 bills, and six \(1 bills (nothing larger). If the bills are selected one by one in random order, what is the probability that at least two bills must be selected to obtain a first \)10 bill?

Short Answer

Expert verified

The probability that at least two bills must be selected to obtain a first $10 bill is 0.67.

Step by step solution

01

Given information

The number of $10 bills that a wallet contains is 5.

The number of $5 bills that a wallet contains is 4.

The number of $1 bills that a wallet contains is 6.

02

Compute the probability

From the provided information, the total number of bills is,

\(5 + 4 + 6 = 15\)

Let X represents the number of trials to select the first $10 bill.

The probability of selecting a $10 bill is \(\frac{5}{{15}}\).

The probability that at least two bills must be selected to obtain a first $10 bill is computed as,

\(\begin{aligned}P\left( {X \ge 2} \right) &= 1 - P\left( {X < 2} \right)\\ &= 1 - P\left( {X = 1} \right)\\ &= 1 - \left( {\frac{5}{{15}}} \right){\left( {1 - \frac{5}{{15}}} \right)^{1 - 1}}\\ &= 1 - \frac{1}{3}\\ &= 1 - 0.33\\ &= 0.67\end{aligned}\)

Therefore, the probability that at least two bills must be selected to obtain a first $10 bill is0.67.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

An insurance company offers four different deductible levels鈥攏one, low, medium, and high鈥攆or its home owner鈥檚 policy holders and three different levels鈥攍ow, medium, and high鈥攆or its automobile policyholders. The accompanying table gives proportions for the various categories of policyholders who have both types of insurance. For example, the proportion of individuals with both low homeowner鈥檚 deductible and low auto deductible is .06(6% of all such individuals).

贬辞尘别辞飞苍别谤鈥檚

Auto N L M H

L .04 .06 .05 .03

M .07 .10 .20 .10

H .02 .03 .15 .15

Suppose an individual having both types of policies is randomly selected.

a. What is the probability that the individual has a medium auto deductible and a high homeowner鈥檚 deductible?

b. What is the probability that the individual has a low auto deductible? A low homeowner鈥檚 deductible?

c. What is the probability that the individual is in the same category for both auto and homeowner鈥檚 deductibles?

d. Based on your answer in part (c), what is the probability that the two categories are different?

e. What is the probability that the individual has at least one low deductible level?

f. Using the answer in part (e), what is the probability that neither deductible level is low?

In Exercise\({\rm{59}}\), consider the following additional information on credit card usage: \({\rm{70\% }}\)of all regular fill-up customers use a credit card. \({\rm{50\% }}\) of all regular non-fill-up customers use a credit card. \({\rm{60\% }}\) of all plus fill-up customers use a credit card. \({\rm{50\% }}\) of all plus non-fill-up customers use a credit card. \({\rm{50\% }}\) of all premium fill-up customers use a credit card. \({\rm{40\% }}\) of all premium non-fill-up customers use a credit card. Compute the probability of each of the following events for the next customer to arrive (a tree diagram might help).

a. {plus and fill-up and credit card}

b. {premium and non-fill-up and credit card}

c. {premium and credit card}

d. {fill-up and credit card}

e. {credit card}

f. If the next customer uses a credit card, what is the probability that premium was requested?

Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S).Consider observing the direction for each of three successive vehicles.

a. List all outcomes in the event Athat all three vehicles go in the same direction.

b. List all outcomes in the event Bthat all three vehicles take different directions.

c. List all outcomes in the event Cthat exactly two of the three vehicles turn right.

d. List all outcomes in the event Dthat exactly two vehicles go in the same direction.

e. List outcomes in D鈥�, C\( \cup \)D, and C\( \cap \)D.

Refer back to the series-parallel system configuration introduced in, and suppose that there are only two cells rather than three in each parallel subsystem eliminate cells 3 and\({\bf{6}}\), and renumber cells \(4\) and \(5\) as \(3\) and \(4\). The probability that system lifetime exceeds t0 is easily seen to be \(.{\bf{9639}}\). To what value would \(.9\) have to be changed in order to increase the system lifetime reliability from \(.{\bf{9639}}\)to \(.{\bf{99}}\)? (Hint: Let P(Ai ) 5 p, express system reliability in terms of p, and then let x 5 p2 .)

Consider independently rolling two fair dice, one red and the other green. Let A be the event that the red die shows \({\rm{3}}\) dots, B be the event that the green die shows \({\rm{4}}\) dots, and C be the event that the total number of dots showing on the two dice is \({\rm{7}}\). Are these events pairwise independent (i.e., are \({\rm{A}}\) and \({\rm{B}}\) independent events, are \({\rm{A}}\) and \({\rm{C}}\) independent, and are \({\rm{B}}\) and \({\rm{C}}\) independent)? Are the three events mutually independent?
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.