4. Although there is some controversy, tongue rolling (the ability to roll the e

Question

4. Although there is some controversy, tongue rolling (the ability to roll the edges of the tongue into a loop) is generally thought to be a genetic trait. Another genetic trait is earlobe attachment. Some people have the earlobe attached to the side of the head, others have earlobes that hang freely. In a class of 80 students, 38 could not roll their tongue, 31 had attached earlobes, and 15 could roll their tongues and had attached earlobes. A student is randomly selected from the class, and whether or not the student can roll his or her tongue and whether or not his or her earlobe is attached are observed. Let T represent the event that the selected student can roll his or her tongue and E earlobes. Symbolically denote the following events and identify the number of students represented by each represent the event that the student has attached a. The student can roll his or her tongue b. The student can neither roll his or her tongue nor has attached earlobes. c. The student has attached earlobes but cannot roll his or her tongue d·The student can roll his or her tongue or has attached earlobes but not both.

Explanation / Answer

a) number of students who can roll his or her tongue =80- who can not =80-38=42

b)student who neither can roll tongue nor attached earlopes =80-who can do at least one

=80-(42+31-15)=22

c)

student with attached earlobe but can not roll his or her tongue =have attached earlobe-can do both =31-15=16

d)

not both =who can do at least one -can do both =(42+31-15)-15=43

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