Question

150 students who play musical instruments were surveyed about their music. 75 students were from CBE (College of Business and Economics) and 75 were from COFAC (College of Fine Arts and Communication). Each student said whether s/he plays the guitar (53 1/3%, or 0.533333 of the total) or a band instrument (46 2/3%, or 0.4666666). Of the CBE students, 2/3 play guitar.

1. How many CBE students play a band instrument? Give a number of students, not a %.

2. If I choose a student randomly from the full sample, what is the probability that I get a student from COFAC?

3. If I choose a student randomly from the full sample, what is the probability that I get a student who plays the guitar?

4. If I choose a student at random from this group of 150, what is the probability that she is a guitar player from COFAC?

Answer 1

To answer the student's questions, 25 CBE students play a band instrument. The probability of choosing a COFAC student from the full sample is 0.5 while that of choosing a guitar player is 0.533333. Finally, the probability of randomly selecting a guitar player from COFAC is 1/3.

Step-by-step explanation:

To solve the student's query, we need to calculate the number of CBE students who play a band instrument, the probability of selecting a COFAC student, the probability of selecting a guitar player, and the probability of selecting a guitar player from COFAC out of the full sample of 150 students.

1. To find the number of CBE students who play a band instrument, we use the fact that 2/3 of the CBE students play the guitar. This means that 1/3 do not play the guitar. Since there are 75 CBE students, the number playing a band instrument would be ⅓ × 75, which is 25.
2. The probability of selecting a student from COFAC is the number of COFAC students divided by the total number of students. Since COFAC has 75 students out of 150, the probability is ½ or 0.5.
3. The probability of selecting a student who plays the guitar is 53 1/3% of the total or 0.533333, as given.
4. To find the probability of choosing a guitar player from COFAC, we first need the number of COFAC guitar players. Since we know that 2/3 of CBE students play guitar, then 1/3 of these 75 students play a band instrument. Hence, 75 - (1/3 × 75) or 50 COFAC students play the guitar. The probability is therefore 50/150 or 1/3.