At Technodynamics, Inc., a randomly-selected hiring committee of 4 people is formed from a group of 4 employees in marketing and 5 employees in management. a) Find the probability that the committee has exactly 3 employees from marketing. b) Find the probability that the committee has at least one employee from marketing. c) Find the probability that the committee has at most one employee from management. Using combination notation, set up the expression that can be used to find the total number of possible committees. (18 The total number of possible committees can be written as a) The probability that the committee has exactly 3 employees from marketing is (Round to four decimal places as needed.) b) The probability that the committee has at least one employee from marketing is (Round to four decimal places as needed.) c) The probability that the committee has at most one employee from management is (Round to four decimal places as needed.)
At Technodynamics, Inc., a randomly-selected hiring committee of 4 people is formed from a group of 4 employees in marketing and 5 employees in management. a) Find the probability that the committee has exactly 3 employees from marketing. b) Find the probability that the committee has at least one employee from marketing. c) Find the probability that the committee has at most one employee from management. Using combination notation, set up the expression that can be used to find the total number of possible committees. (18 The total number of possible committees can be written as a) The probability that the committee has exactly 3 employees from marketing is (Round to four decimal places as needed.) b) The probability that the committee has at least one employee from marketing is (Round to four decimal places as needed.) c) The probability that the committee has at most one employee from management is (Round to four decimal places as needed.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Technodynamics, Inc. Committee Selection Probability Problem
**Problem Statement:**
At Technodynamics, Inc., a randomly-selected hiring committee of 4 people is formed from a group of 4 employees in marketing and 5 employees in management.
a) Find the probability that the committee has exactly 3 employees from marketing.
b) Find the probability that the committee has at least one employee from marketing.
c) Find the probability that the committee has at most one employee from management.
---
**Using combination notation, set up the expression that can be used to find the total number of possible committees.**
---
**Solution:**
The total number of possible committees can be written as \( \binom{n}{k} \).
\[
\binom{\Box}{} \binom{}{}
\]
a) The probability that the committee has exactly 3 employees from marketing is \( \Box \).
(Round to four decimal places as needed.)
b) The probability that the committee has at least one employee from marketing is \( \Box \).
(Round to four decimal places as needed.)
c) The probability that the committee has at most one employee from management is \( \Box \).
(Round to four decimal places as needed.)
---
This problem involves calculating probabilities using combinations. The approach involves defining the total sample space and the success cases for each condition given, then using the combination formula to find the number of possible committees fitting each criterion. Finally, the probability is derived by dividing the number of successful outcomes by the total number of possible committees.
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Transcribed Image Text:---
### Technodynamics, Inc. Committee Selection Probability Problem
**Problem Statement:**
At Technodynamics, Inc., a randomly-selected hiring committee of 4 people is formed from a group of 4 employees in marketing and 5 employees in management.
a) Find the probability that the committee has exactly 3 employees from marketing.
b) Find the probability that the committee has at least one employee from marketing.
c) Find the probability that the committee has at most one employee from management.
---
**Using combination notation, set up the expression that can be used to find the total number of possible committees.**
---
**Solution:**
The total number of possible committees can be written as \( \binom{n}{k} \).
\[
\binom{\Box}{} \binom{}{}
\]
a) The probability that the committee has exactly 3 employees from marketing is \( \Box \).
(Round to four decimal places as needed.)
b) The probability that the committee has at least one employee from marketing is \( \Box \).
(Round to four decimal places as needed.)
c) The probability that the committee has at most one employee from management is \( \Box \).
(Round to four decimal places as needed.)
---
This problem involves calculating probabilities using combinations. The approach involves defining the total sample space and the success cases for each condition given, then using the combination formula to find the number of possible committees fitting each criterion. Finally, the probability is derived by dividing the number of successful outcomes by the total number of possible committees.
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