Answer:
1.79 %.
Step-by-step explanation:
you have to calculate the probability of a series of events before you can calculate the final probability.
The first event is that the band plays on Friday.
If there are 8 bands, but only 5 play on Friday, then the probability that they will play on Friday is
5/8
Now, the second event that they are the last ones is 1/5, since they are 5 bands.
Therefore the probability that they will play on Saturday and last is
5/8 * 1/5 = 1/8
Now, for the rival band it would be, knowing that on Friday there is already a quota assigned and one band less, the probability that they will play that day is
4/7
as they play before the other group, it would be 1/4, as there is already a quota assigned.
The final probability would then be:
4/7 * 1/4 = 1/7
Now the probability that the band gives the last performance on Friday night and your rival band performs immediately before them, is:
1/8 * 1/7 = 0.0179
That is 1.79 %.
