If a student may do more than one​ job, then what is the probability that the instructor will choose all students of the same​ sex?

Question

27) Refer to the demographic information shown to the right that has been collected by 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 all students of the same​ sex?

Total number of students in the class	52		Number of boys	19
Number of girls	33
Number of Freshman	9
Number of Sophomores	16
Number of Juniors	10
Number of Seniors	17

There is a ___% probability that the instructor will choose all students of the same sex.

​(Round the final answer to one decimal place as needed. Round all intermediate values to three decimal places as​ needed.)

Answer 1

This is again a binomial distribution problem with p=33/52.

What is required is the probability of 2 independent events, namely all girls OR all boys.

This will be given by the 0 term PLUS the 3 term in the binomial density.