Question

60 musicians applied for a job at a music school. 14 of the musicians play both guitar and drums, 28 play drums, 18 play the guitar. What is the probability that the applicant who gets the job plays drums or guitar?

Answer 1

The probability is 8 over 15.

Explanation:

14 of the musicians play both guitar and drums, 28 play drums, 18 play the guitar.

It means n(G and D)=14, n(D)=28, n(G)=18.

Using the formula of Union:-

n(G or D) = n(G) + n(D) - n(G and D).

n(G or D) = 18 + 28 - 14.

n(G or D) = 32.

It says 60 musicians applied for a job at a music school. So n(U)=60.

the probability that the applicant who gets the job plays drums or guitar is = n(G or D)/n(U) = 32/60 = 8/15.

Hence, the probability is 8 over 15.