Math Question Help

Question

Out of 8 bars in a town which offer to pay bands to perform, one is run by a sleazy operator who does not pay bands after they play, while the other seven bars pay the promised amount.

3a) If a band, which is on a long tour and not cognizant of the area, selects one of the bars at random to play at, what is the probability that it does not get paid?

3b) What is the probability that the band plays two gigs at this town, 3 weeks apart, and does not get paid either time? Assume the band is offered a gig at a random location each time.

Answer 1

One out of the eight bars will not pay the band. So, the band has a 1 in 8 = 1/8 probability of not getting paid.

 

If the band returns a second time, they have another 1/8 probability of not getting paid that time.

 

 

Since the events are independent, multiply them to figure out the probability of both events (not getting paid the first time and not getting paid the second time) happening:

 

1/8 × 1/8 = 1/64

 

 

The band has a 1 in 64 or 1/64 probability of not getting paid either time.