Question

7. Chapter 4 review (6 points) What is the number of permutations of 8 things taken 2 at a time? What is the number of combinations of 9 things taken 6 at a time? (Conditional probability) A survey is taken of Music Majors and Art Majors to measure their skill at math. The results are in this table: Skill at Math Good Not Good Major Music Major 10 Art Major 27 What is the probability that a student is Good in Math given that the student is an art major?

Answer 1

(a) 8P2 =

$_{8}P_{2} = \frac{8!}{(8-2)!} = 56$

(b) combinations of 9 things taken 6 at a time

$_{9}C_{6} = \frac{9!}{6! (9-6)!} = 84$

(c) P(good in maths/ art major) = P(good in maths and art major) / P(art major)

P(good in maths and art major) = 5/27

P (art major) = 9/27

P(good in maths/ art major) = (5/27) / (9/27) = 5/9 = 0.56

P(good in maths/ art major) = 5/9 = 0.56