/*! 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} Q11E Suppose that 10 cards, of which ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q11E (page 51)

Suppose that 10 cards, of which five are red and five are green, are placed at random in 10 envelopes, of which five are red and five are green. Determine the probability that exactly x envelopes will contain a card with a matching colour (x = 0, 1, ... , 10).

Short Answer

Expert verified

The probability that exactly x envelopes will contain a card with a matching colour\(\frac{{\left( {^5{C_{\frac{r}{2}}}} \right)\left( {^5{C_{_{\frac{r}{2}}}}} \right)}}{{10!}}\;\;;\;\forall r = 0,2,...,10\). In terms of \(\frac{{\left( {^5{C_x}} \right)\left( {^5{C_x}} \right)}}{{10!}}\;;\;\forall x\left( { = 2r} \right) = 0,1,...,10\)

Step by step solution

01

Given information

Number of red and green coloured envelopes is 5 each. Also, the number of red and green coloured letters is 5 each.

02

Compute the counts

The total number of favourable outcomes are \(10!\)

On selecting 5 red or 5 green envelopes, number of red or green envelopes that could be placed in right colour combination is,

\(\begin{array}{l}{\bf{r = 0,1,2,3,4,5}}\\{\bf{g = 0,1,2,3,4,5}}\end{array}\)

Hence,

\(\begin{array}{c}x = 2r\\ = 2g\end{array}\)

And\(x = 0,2,4,...,10\).

The probability that x envelope would contain the right colour combination card is,

\(\frac{{^5{C_x}^{5 - x}{C_x}}}{{10!}} = \frac{{^5{C_x}^5{C_x}}}{{10!}}\)

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

Suppose that four guests check their hats when they arrive at a restaurant, and that these hats are returned to them in a random order when they leave. Determine the probability that no guest will receive the proper hat.

Suppose that one card is to be selected from a deck of 20 cards that contains 10 red cards numbered from 1 to 10 and 10 blue cards numbered from 1 to 10. Let A be the event that a card with an even number is selected, let B be the event that a blue card is selected, and let C be the event that a card with a number less than 5 is selected. Describe the sample space S and describe each of the following events both in words and as subsets of S:

a. \({\bf{A}} \cap {\bf{B}} \cap {\bf{C}}\)

b. \({\bf{B}} \cap {{\bf{C}}^{\bf{C}}}\)

c. \({\bf{A}} \cup {\bf{B}} \cup {\bf{C}}\)

d. \({\bf{A}} \cap {\bf{(B}} \cup {\bf{C)}}\)

e. \({{\bf{A}}^{\bf{c}}} \cap {{\bf{B}}^{\bf{c}}} \cap {{\bf{C}}^{\bf{c}}}\)

Question:Suppose that a point (X,Y)is chosen at random from the regionSin thexy-plane containing all points (x,y) such thatx鈮�0,y鈮�0, and 4y+x鈮�4.

a. Determine the joint p.d.f. ofXandY.

b. Suppose that\({{\bf{S}}_{\bf{0}}}\)is a subset of the regionShaving area伪and determine\({\bf{Pr}}\left( {\left( {{\bf{X,Y}}} \right) \in {{\bf{S}}_{\bf{0}}}} \right)\).

For two arbitrary events A and B, prove that

\({\bf{Pr}}\left( {\bf{A}} \right){\rm{ }} = {\rm{ }}{\bf{Pr}}({\bf{A}} \cap {\bf{B}}){\rm{ }} + {\rm{ }}{\bf{Pr}}({\bf{A}} \cap {{\bf{B}}^c}).\)

A box contains 24 light bulbs, of which four are defective. If a person selects four bulbs from the box at random, without replacement, what is the probability that all four bulbs will be defective?
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

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.