At Technodynamics, Inc., a randomly-selected hiring committee of 3 people is for

Question

At Technodynamics, Inc., a randomly-selected hiring committee of 3 people is formed from a group of 5 employees in marketing and 4 employees in management. a) Find the probability that the committee has exactly 2 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. The total number of possible committees can be written as a) The probability that the committee has exactly 2 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

Explanation / Answer

Solution:

total number ofemployees = 5 + 4 = 9

number of employees from marketing = 5

number of employee from management = 4

total number of possible commettees = 9C3 = 84

( a )

probability that the committee has exactly 2 employees from marketing = 5C2 * 4C1 / 9C3

= 10*4/84

= 40/84

= 0.4761

( b )

probability that the committee has atleast employees from marketing = (( 5C1 * 4C2) +(5C2 * 4C1 ) + 5C3) /  9C3

= ( 5*6+10*4+10) / 84

= (30+40+10 ) / 84

= 80/84

= 0.9523

( c )

probability that the committee has atmost employees from marketing = (( 5C0 * 4C3) +(5C1* 4C2 ))  /  9C3 = ( 4 + 5*6)/ 84

= 34/84

= 0.4047

  

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