Question

In a class of 27 students, 11 students play an instrument, 14 students have a job,

and 8 students play an instrument and have a job. Find the probability that:

a) a student has a job but doesn't play an instrument.

b) a student doesn't have a job and doesn't play an instrument.​

Answer 1

.22222

.37037

Explanation:

I=instrument

J=job

a.)

to have a job and not play instrument is equal to J∩I'

j= J∩I+J∩I'

14=8+J∩I'

J∩I'=6

which in terms of a probability is 6/27= 2/9=.22222

b.)

27-I∪J

I∪J=I+J-I∩J

11+14-8=17

27-17=10

10/27= .37037