I have a class of seven students named: Abby, Brian, Charles, Dorothy, Elaina, F

Question

I have a class of seven students named: Abby, Brian, Charles, Dorothy, Elaina, Francis, Geoff. Call event A when a student has an ‘a’ in their name. Call event E when a student has an ‘e’ in their name. Call event I when a student has an ‘i’ in their name. Call all students in the class the sample space S. I am going to randomly select one student from the class to help me distribute materials each week.

From the seven students in my class described above, if I randomly select two students from the class to receive two awards, calculate the following probabilities. Show your work.

Both students selected have an ‘a’ in their name (a student is only eligible for one award, i.e., without replacement)

Both students selected have an ‘a’ in their name (a student is eligible to receive both awards, i.e., with replacement)

Explanation / Answer

total 7 students
There are 5 students in a class with 'a' in their name.

a)
Two different students from 7 can be selected in 7C2 ways
Two different students from 5 eligible can be selected in 5C2 ways

Required probability = 5C2/7C2 = 0.4762

b)
Two students from 7 with replacement can be selected in 7*7 ways
Two students from 5 with replacement can be selected in 5*5 ways

Required probability = 25/49 = 0.5102

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.