amira recorded the grade - level and instrument of everyone in the middle school school of rock…

amira recorded the grade - level and instrument of everyone in the middle school school of rock below.\nseventh grade students\n|instrument|# of students|\n|--|--|\n|guitar|6|\n|bass|2|\n|drums|15|\n|keyboard|2|\neighth grade students\n|instrument|# of students|\n|--|--|\n|guitar|10|\n|bass|8|\n|drums|8|\n|keyboard|13|\nbased on these results, express the probability that an eighth grader chosen at random will play an instrument other than keyboard as a fraction in simplest form.

amira recorded the grade - level and instrument of everyone in the middle school school of rock below.\nseventh grade students\n|instrument|# of students|\n|--|--|\n|guitar|6|\n|bass|2|\n|drums|15|\n|keyboard|2|\neighth grade students\n|instrument|# of students|\n|--|--|\n|guitar|10|\n|bass|8|\n|drums|8|\n|keyboard|13|\nbased on these results, express the probability that an eighth grader chosen at random will play an instrument other than keyboard as a fraction in simplest form.

Answer

Explanation:

Step1: Calculate total number of eighth - graders

Add the number of students for each instrument in eighth - grade. $10 + 8+8 + 13=39$.

Step2: Calculate number of eighth - graders who play non - keyboard instruments

Add the number of students for guitar, bass and drums in eighth - grade. $10 + 8+8 = 26$.

Step3: Calculate the probability

The probability $P$ that an eighth - grader chosen at random plays an instrument other than keyboard is the number of eighth - graders who play non - keyboard instruments divided by the total number of eighth - graders. So $P=\frac{26}{39}$.

Step4: Simplify the fraction

Find the greatest common divisor (GCD) of 26 and 39. The GCD of 26 and 39 is 13. Divide both the numerator and denominator by 13: $\frac{26\div13}{39\div13}=\frac{2}{3}$.

Answer:

$\frac{2}{3}$