Problema Solution
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 canceled, and the band figures there is a 1/6 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?
Answer provided by our tutors
The probability that the festival is not cancelled is:
P(Festival not cancelled) = 1 - P(Festival in cancelled)
P(Festival not cancelled) = 1 - 3/8
P(Festival not cancelled) = 5/8
The probability that the band plays is:
P(The band is able to play) = 1 - P(The band is not able to play)
P(The band is able to play) = 1 - 1/6
P(The band is able to play) = 5/6
Now we need to find the probability that "The festival is not cancelled" and "The band is able to play".
Since the 2 events "The festival is not cancelled" and "The band is able to play" are independent we have:
P(The band ends up playing the festival) = P(Festival is not cancelled)*P(The band is able to play)
P(The band ends up playing the festival) = (5/8)*(5/6)
P(The band ends up playing the festival) = 25/48
P(The band ends up playing the festival) = 0.5208
The probability that the band ends up playing the festival is 25/48 or 0.5208.