Refer to the demographic infomation shown to the right that has been collected b

Question

Refer to the demographic infomation shown to the right that has been collected by Total number of students in the class an instructor after surveying her class The instructor randomly chooses one student to pass out papers, one student to clean the chalkboard, and one student to empty the trash. If a student may do more than one job, then what is the probability that the instructor will choose at most one senior to do the jobs? 50 17 Number of girls Number of Freshman Number of Sophomores Number of Juniors Number of Seniors 18 15 There is a%probablity that the instructor wl choose at most one senior to do the jobs Round the final answer to one decimal place as needed Round all intermediate values to three decimal places as needed

Explanation / Answer

a student may do more than one job , it means repeatition is allowed

seniors = 15

except seniors remaining number = 50-15

= 35

P(at most one senior) = P(no senior) + P(one senior)

= (35*35*35) / (50*50*50) + {15*35*35*(3!/2!)} /(50*50*50)

here 3! / 2! is used for rearrangement of seniors and others (3! for arrangement of 3 people , divided by 2! means 2 people are of same group i.e not seniors)

P(at most one senior) = 0.784

=0.784*100

= 78.4% (answer)

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