150 students who play musical instruments were surveyed about their music. 75 st

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?

Explanation / Answer

From the given data, the following Table is formed:

                                     CBE                                COFAC                  Total

guitar                             50                                        30                      80

band                             25                                        45                      70

Total 75 75                      150

EXPLANATION:

Guitar = 53 1/3 % i.e. 0.5333 of 150.. = 150 X 0.5333= 80

Band = 46 2/3 % i.e., 0.46666 of 150 = 150 X 0.4666 = 70

(1) CBE & Band = 25

(2) P(COFAC) = 75/150 = 0.50

(3) P(guitar) = 80/150 = 0.5333

(4) P(guitar & COFAC) = 30/150 = 0.2

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