Music/Math Question

Question

Several months in advance, a festival books a band to play. At the moment that the band is booked, the festival figures that there is a 3/8 chance that the festival will be cancelled, and the band figures there is a 1/5 chance that it won’t be able to play the festival and would have to cancel. Assuming both the festival and the band figure correctly, what is the probability that, as of the booking, the band ends up playing the
festival? (Your answer should be a fraction; assume cancellations are independent.)

Answer 1

There are two events that might interfere with the band playing. 

 

Event A. The festival could be cancelled (P(A) = 3/8)

Event B.  The band might have to cancel (P(B) = 1/5). 

 

Since the events are independent, it's also possible that both could happen.  So you want to figure the probability of one of both of the two events happening.

 

That's P(A or B), which is equal to P(A) + P(B) - P(A and B) = 3/8 + 1/5 - 3/8 * 1/5 = 15/40 + 8/40 - 3/40 = 20/40 = 1/2.

 

Therefore the probability that band WON'T play is 1/2. 

 

The probability that the band WILL play is 1 - P(A or B) = 1 - 1/2 = 1/2