Independent Probability

Question

A band has a gig tentatively to play a festival. There is a 3/8 chance that the festival cancels; there is a 1/5 chance that the band cancels. What is the probability that the band ends up playing the festival? (Your answer should be a fraction; assume cancellations are independent)

Answer 1

You want to find the probability that the festival cancels OR the band cancels. That will tell you the probability that they DON'T play.  Then subtract that from 1 to get the probability that they DO play.

 

By the formula for the probability of the union of independent events, the probability that they don't play is equal to P(festival cancels) + P(band cancels) - P (festival cancels AND band cancels).

 

So that's 3/8 + 1/5 - (3/8)(1/5) = 15/40 + 8/40 - 3/40 = 20/40 = 1/2

 

So the probability that they DON'T play is 1/2.  Therefore the probability that they DO play is 1 - 1/2 = 1/2.