Stats Question related to probability

Question

A survey about favorite music genre was given to a class. Three students said that their favorite genre was Electronic Dance, nine students said Alternative Rock, eight students said Pop, five students said Classical, and six students said Country. (Each student only gave one favorite music genre.)  

1. If two students are randomly selected from the class with replacement, what is the chance that one has a favorite of Electronic Dance and the other has a favorite of Country? (Give answer as reduced fraction, decimal w/4 places, or percentage w/2 places and percent sign.)

2.If two students are randomly selected from the class without replacement, what is the chance that both students have the same favorite music genre? (Give answer as reduced fraction, decimal w/4 places, or percentage w/2 places and percent sign.)

Answer 1

Electronic Dance = 3 students

Alternative Rock = 9 students

Pop = 8 students

Classical = 5 students

Country = 6 students

Total number of students surveyed is 31 students.

P(Electronic Dance and Country) = (3/31)*(6/31) = 0.019 or 1.9%

The probability that the first student likes Electronic Dance and the second student likes Country is 0.019.

P(Both like Electronic Dance) = (3/31)*(2/30) = 6/930 = 0.0065 or 0.65%

P(Both like Alternative Rock) = (9/31)*(8/30) = 72/930 = 0.077 or 7.7%

P(Both like Pop) = (8/31)*(7/30) = 56/930 = 0.060 = 6.0%

P(Both like Classical) = (5/31)*(4/30) = 20/930 = 0.022 = 2.2%

P(Both like Country) = (6/31)*(5/30) = 30/930 = 0.032 = 3.2%

P(Both like the Same Music) = 0.0065 + 0.077 + 0.060 + 0.022 + 0.032 = 0.1975 ≈ 0.20 or 20%

The probability that both students selected like the same music genre is about 0.20.