Question

seventh grade students instrument # of students guitar bass drums keyboard 12 3 10 5 eighth grade students instrument # of students guitar bass drums keyboard 4 3 6 2 based on these results, express the probability that a student chosen at random will play an instrument other than guitar as a fraction in simplest form.

Explanation:

Step1: Calculate total number of students

Sum students of all non - guitar instruments in both grades. For seventh grade: \(5 + 10+3=18\). For eighth grade: \(2 + 6+3 = 11\). Total non - guitar students is \(18 + 11=29\).

Step2: Calculate total number of students in both grades

Sum all students in both grades. Seventh grade total: \(5 + 10+3 + 12=30\). Eighth grade total: \(2+6 + 3+4 = 15\). Overall total is \(30+15 = 45\).

Step3: Calculate probability

Probability \(P=\frac{\text{Number of non - guitar students}}{\text{Total number of students}}=\frac{29}{45}\). Since 29 and 45 have no common factors other than 1, it is in simplest form.

Answer:

\(\frac{29}{45}\)